Reference documentation for deal.II version Git 03f4796af1 2021-03-01 10:26:03 -0500
FEFaceValues< dim, spacedim > Class Template Reference

#include <deal.II/fe/fe.h>

Inheritance diagram for FEFaceValues< dim, spacedim >:
[legend]

## Public Member Functions

FEFaceValues (const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &quadrature, const UpdateFlags update_flags)

FEFaceValues (const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe, const hp::QCollection< dim - 1 > &quadrature, const UpdateFlags update_flags)

FEFaceValues (const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &quadrature, const UpdateFlags update_flags)

FEFaceValues (const FiniteElement< dim, spacedim > &fe, const hp::QCollection< dim - 1 > &quadrature, const UpdateFlags update_flags)

template<bool level_dof_access>
void reinit (const TriaIterator< DoFCellAccessor< dim, spacedim, level_dof_access >> &cell, const unsigned int face_no)

template<bool level_dof_access>
void reinit (const TriaIterator< DoFCellAccessor< dim, spacedim, level_dof_access >> &cell, const typename Triangulation< dim, spacedim >::face_iterator &face)

void reinit (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no)

void reinit (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const typename Triangulation< dim, spacedim >::face_iterator &face)

const FEFaceValues< dim, spacedim > & get_present_fe_values () const

const Tensor< 1, spacedim > & boundary_form (const unsigned int i) const

const std::vector< Tensor< 1, spacedim > > & get_boundary_forms () const

unsigned int get_face_index () const

std::size_t memory_consumption () const

template<class Archive >
void serialize (Archive &ar, const unsigned int version)

These fields are filled by the finite element.

const doubleshape_value (const unsigned int function_no, const unsigned int point_no) const

double shape_value_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const

const Tensor< 1, spacedim > & shape_grad (const unsigned int function_no, const unsigned int quadrature_point) const

Tensor< 1, spacedim > shape_grad_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const

const Tensor< 2, spacedim > & shape_hessian (const unsigned int function_no, const unsigned int point_no) const

Tensor< 2, spacedim > shape_hessian_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const

const Tensor< 3, spacedim > & shape_3rd_derivative (const unsigned int function_no, const unsigned int point_no) const

Tensor< 3, spacedim > shape_3rd_derivative_component (const unsigned int function_no, const unsigned int point_no, const unsigned int component) const

template<class InputVector >
void get_function_values (const InputVector &fe_function, std::vector< typename InputVector::value_type > &values) const

template<class InputVector >
void get_function_values (const InputVector &fe_function, std::vector< Vector< typename InputVector::value_type >> &values) const

template<class InputVector >
void get_function_values (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< typename InputVector::value_type > &values) const

template<class InputVector >
void get_function_values (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Vector< typename InputVector::value_type >> &values) const

template<class InputVector >
void get_function_values (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< typename InputVector::value_type >> values, const bool quadrature_points_fastest) const

template<class InputVector >
void get_function_gradients (const InputVector &fe_function, std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> &gradients) const

template<class InputVector >
void get_function_gradients (const InputVector &fe_function, std::vector< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> &gradients) const

template<class InputVector >
void get_function_gradients (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> &gradients) const

template<class InputVector >
void get_function_gradients (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> gradients, const bool quadrature_points_fastest=false) const

Hessian matrices and Laplacians of global finite element fields

template<class InputVector >
void get_function_hessians (const InputVector &fe_function, std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> &hessians) const

template<class InputVector >
void get_function_hessians (const InputVector &fe_function, std::vector< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> &hessians, const bool quadrature_points_fastest=false) const

template<class InputVector >
void get_function_hessians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> &hessians) const

template<class InputVector >
void get_function_hessians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> hessians, const bool quadrature_points_fastest=false) const

template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, std::vector< typename InputVector::value_type > &laplacians) const

template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, std::vector< Vector< typename InputVector::value_type >> &laplacians) const

template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< typename InputVector::value_type > &laplacians) const

template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Vector< typename InputVector::value_type >> &laplacians) const

template<class InputVector >
void get_function_laplacians (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< std::vector< typename InputVector::value_type >> &laplacians, const bool quadrature_points_fastest=false) const

template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> &third_derivatives) const

template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, std::vector< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> &third_derivatives, const bool quadrature_points_fastest=false) const

template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> &third_derivatives) const

template<class InputVector >
void get_function_third_derivatives (const InputVector &fe_function, const ArrayView< const types::global_dof_index > &indices, ArrayView< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> third_derivatives, const bool quadrature_points_fastest=false) const

Cell degrees of freedom
std_cxx20::ranges::iota_view< unsigned int, unsigned intdof_indices () const

std_cxx20::ranges::iota_view< unsigned int, unsigned intdof_indices_starting_at (const unsigned int start_dof_index) const

std_cxx20::ranges::iota_view< unsigned int, unsigned intdof_indices_ending_at (const unsigned int end_dof_index) const

Geometry of the cell
std_cxx20::ranges::iota_view< unsigned int, unsigned intquadrature_point_indices () const

const Point< spacedim > & quadrature_point (const unsigned int q) const

const std::vector< Point< spacedim > > & get_quadrature_points () const

double JxW (const unsigned int quadrature_point) const

const std::vector< double > & get_JxW_values () const

const DerivativeForm< 1, dim, spacedim > & jacobian (const unsigned int quadrature_point) const

const std::vector< DerivativeForm< 1, dim, spacedim > > & get_jacobians () const

const DerivativeForm< 2, dim, spacedim > & jacobian_grad (const unsigned int quadrature_point) const

const std::vector< DerivativeForm< 2, dim, spacedim > > & get_jacobian_grads () const

const Tensor< 3, spacedim > & jacobian_pushed_forward_grad (const unsigned int quadrature_point) const

const std::vector< Tensor< 3, spacedim > > & get_jacobian_pushed_forward_grads () const

const DerivativeForm< 3, dim, spacedim > & jacobian_2nd_derivative (const unsigned int quadrature_point) const

const std::vector< DerivativeForm< 3, dim, spacedim > > & get_jacobian_2nd_derivatives () const

const Tensor< 4, spacedim > & jacobian_pushed_forward_2nd_derivative (const unsigned int quadrature_point) const

const std::vector< Tensor< 4, spacedim > > & get_jacobian_pushed_forward_2nd_derivatives () const

const DerivativeForm< 4, dim, spacedim > & jacobian_3rd_derivative (const unsigned int quadrature_point) const

const std::vector< DerivativeForm< 4, dim, spacedim > > & get_jacobian_3rd_derivatives () const

const Tensor< 5, spacedim > & jacobian_pushed_forward_3rd_derivative (const unsigned int quadrature_point) const

const std::vector< Tensor< 5, spacedim > > & get_jacobian_pushed_forward_3rd_derivatives () const

const DerivativeForm< 1, spacedim, dim > & inverse_jacobian (const unsigned int quadrature_point) const

const std::vector< DerivativeForm< 1, spacedim, dim > > & get_inverse_jacobians () const

const Tensor< 1, spacedim > & normal_vector (const unsigned int i) const

const std::vector< Tensor< 1, spacedim > > & get_normal_vectors () const

Extractors Methods to extract individual components
const FEValuesViews::Scalar< dim, spacedim > & operator[] (const FEValuesExtractors::Scalar &scalar) const

const FEValuesViews::Vector< dim, spacedim > & operator[] (const FEValuesExtractors::Vector &vector) const

const FEValuesViews::SymmetricTensor< 2, dim, spacedim > & operator[] (const FEValuesExtractors::SymmetricTensor< 2 > &tensor) const

const FEValuesViews::Tensor< 2, dim, spacedim > & operator[] (const FEValuesExtractors::Tensor< 2 > &tensor) const

const Mapping< dim, spacedim > & get_mapping () const

const FiniteElement< dim, spacedim > & get_fe () const

UpdateFlags get_update_flags () const

const Triangulation< dim, spacedim >::cell_iterator get_cell () const

CellSimilarity::Similarity get_cell_similarity () const

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int n_subscriptions () const

template<typename StreamType >
void list_subscribers (StreamType &stream) const

void list_subscribers () const

## Static Public Member Functions

static ::ExceptionBaseExcAccessToUninitializedField (std::string arg1)

static ::ExceptionBaseExcFEDontMatch ()

static ::ExceptionBaseExcShapeFunctionNotPrimitive (int arg1)

static ::ExceptionBaseExcFENotPrimitive ()

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

## Public Attributes

const unsigned int dofs_per_cell

## Static Public Attributes

static const unsigned int dimension = dim

static const unsigned int space_dimension = spacedim

static const unsigned int integral_dimension = dim - 1

## Protected Member Functions

void invalidate_present_cell ()

void maybe_invalidate_previous_present_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell)

UpdateFlags compute_update_flags (const UpdateFlags update_flags) const

void check_cell_similarity (const typename Triangulation< dim, spacedim >::cell_iterator &cell)

## Protected Attributes

unsigned int present_face_no

unsigned int present_face_index

const hp::QCollection< dim - 1 > quadrature

std::unique_ptr< const CellIteratorBasepresent_cell

boost::signals2::connection tria_listener_refinement

boost::signals2::connection tria_listener_mesh_transform

const SmartPointer< const Mapping< dim, spacedim >, FEValuesBase< dim, spacedim > > mapping

std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > mapping_data

::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > mapping_output

const SmartPointer< const FiniteElement< dim, spacedim >, FEValuesBase< dim, spacedim > > fe

std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > fe_data

::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > finite_element_output

UpdateFlags update_flags

CellSimilarity::Similarity cell_similarity

## Private Member Functions

void initialize (const UpdateFlags update_flags)

void do_reinit (const unsigned int face_no)

## Detailed Description

### template<int dim, int spacedim = dim> class FEFaceValues< dim, spacedim >

Finite element evaluated in quadrature points on a face.

This class adds the functionality of FEFaceValuesBase to FEValues; see there for more documentation.

Since finite element functions and their derivatives may be discontinuous at cell boundaries, there is no restriction of this function to a mesh face. But, there are limits of these values approaching the face from either of the neighboring cells.

Definition at line 40 of file fe.h.

## ◆ FEFaceValues() [1/4]

template<int dim, int spacedim>
 FEFaceValues< dim, spacedim >::FEFaceValues ( const Mapping< dim, spacedim > & mapping, const FiniteElement< dim, spacedim > & fe, const Quadrature< dim - 1 > & quadrature, const UpdateFlags update_flags )

Constructor. Gets cell independent data from mapping and finite element objects, matching the quadrature rule and update flags.

Definition at line 4680 of file fe_values.cc.

## ◆ FEFaceValues() [2/4]

template<int dim, int spacedim>
 FEFaceValues< dim, spacedim >::FEFaceValues ( const Mapping< dim, spacedim > & mapping, const FiniteElement< dim, spacedim > & fe, const hp::QCollection< dim - 1 > & quadrature, const UpdateFlags update_flags )

Like the function above, but taking a collection of quadrature rules. This allows to assign each face a different quadrature rule. In the case that the collection only contains a single face quadrature, this quadrature rule is use on all faces.

Definition at line 4694 of file fe_values.cc.

## ◆ FEFaceValues() [3/4]

template<int dim, int spacedim>
 FEFaceValues< dim, spacedim >::FEFaceValues ( const FiniteElement< dim, spacedim > & fe, const Quadrature< dim - 1 > & quadrature, const UpdateFlags update_flags )

Constructor. This constructor is equivalent to the other one except that it makes the object use a $$Q_1$$ mapping (i.e., an object of type MappingQGeneric(1)) implicitly.

Definition at line 4711 of file fe_values.cc.

## ◆ FEFaceValues() [4/4]

template<int dim, int spacedim>
 FEFaceValues< dim, spacedim >::FEFaceValues ( const FiniteElement< dim, spacedim > & fe, const hp::QCollection< dim - 1 > & quadrature, const UpdateFlags update_flags )

Like the function above, but taking a collection of quadrature rules. This allows to assign each face a different quadrature rule. In the case that the collection only contains a single face quadrature, this quadrature rule is use on all faces.

Definition at line 4723 of file fe_values.cc.

## ◆ reinit() [1/4]

template<int dim, int spacedim>
template<bool lda>
 void FEFaceValues< dim, spacedim >::reinit ( const TriaIterator< DoFCellAccessor< dim, spacedim, lda >> & cell, const unsigned int face_no )

Reinitialize the gradients, Jacobi determinants, etc for the face with number face_no of cell and the given finite element.

Definition at line 4803 of file fe_values.cc.

## ◆ reinit() [2/4]

template<int dim, int spacedim>
template<bool lda>
 void FEFaceValues< dim, spacedim >::reinit ( const TriaIterator< DoFCellAccessor< dim, spacedim, lda >> & cell, const typename Triangulation< dim, spacedim >::face_iterator & face )

Reinitialize the gradients, Jacobi determinants, etc for face face and cell cell.

Note
face must be one of cell's face iterators.

Definition at line 4833 of file fe_values.cc.

## ◆ reinit() [3/4]

template<int dim, int spacedim>
 void FEFaceValues< dim, spacedim >::reinit ( const typename Triangulation< dim, spacedim >::cell_iterator & cell, const unsigned int face_no )

Reinitialize the gradients, Jacobi determinants, etc for the given face on a given cell of type "iterator into a Triangulation object", and the given finite element. Since iterators into a triangulation alone only convey information about the geometry of a cell, but not about degrees of freedom possibly associated with this cell, you will not be able to call some functions of this class if they need information about degrees of freedom. These functions are, above all, the get_function_value/gradients/hessians/third_derivatives functions. If you want to call these functions, you have to call the reinit variants that take iterators into DoFHandler or other DoF handler type objects.

Definition at line 4845 of file fe_values.cc.

## ◆ reinit() [4/4]

template<int dim, int spacedim>
 void FEFaceValues< dim, spacedim >::reinit ( const typename Triangulation< dim, spacedim >::cell_iterator & cell, const typename Triangulation< dim, spacedim >::face_iterator & face )

Definition at line 4866 of file fe_values.cc.

## ◆ get_present_fe_values()

template<int dim, int spacedim = dim>
 const FEFaceValues& FEFaceValues< dim, spacedim >::get_present_fe_values ( ) const

Return a reference to this very object.

Though it seems that it is not very useful, this function is there to provide capability to the hp::FEValues class, in which case it provides the FEValues object for the present cell (remember that for hp-finite elements, the actual FE object used may change from cell to cell, so we also need different FEValues objects for different cells; once you reinitialize the hp::FEValues object for a specific cell, it retrieves the FEValues object for the FE on that cell and returns it through a function of the same name as this one; this function here therefore only provides the same interface so that one can templatize on FEValues and hp::FEValues).

## ◆ initialize()

template<int dim, int spacedim>
 void FEFaceValues< dim, spacedim >::initialize ( const UpdateFlags update_flags )
private

Do work common to the two constructors.

Definition at line 4741 of file fe_values.cc.

## ◆ do_reinit()

template<int dim, int spacedim>
 void FEFaceValues< dim, spacedim >::do_reinit ( const unsigned int face_no )
private

The reinit() functions do only that part of the work that requires knowledge of the type of iterator. After setting present_cell(), they pass on to this function, which does the real work, and which is independent of the actual type of the cell iterator.

Definition at line 4878 of file fe_values.cc.

## ◆ boundary_form()

template<int dim, int spacedim = dim>
 const Tensor<1, spacedim>& FEFaceValuesBase< dim, spacedim >::boundary_form ( const unsigned int i ) const
inherited

Boundary form of the transformation of the cell at the ith quadrature point. See GlossBoundaryForm.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_boundary_forms flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_boundary_forms()

template<int dim, int spacedim>
 const std::vector< Tensor< 1, spacedim > > & FEFaceValuesBase< dim, spacedim >::get_boundary_forms ( ) const
inherited

Return the list of outward normal vectors times the Jacobian of the surface mapping.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_boundary_forms flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4648 of file fe_values.cc.

## ◆ get_face_index()

template<int dim, int spacedim = dim>
 unsigned int FEFaceValuesBase< dim, spacedim >::get_face_index ( ) const
inherited

Return the index of the face selected the last time the reinit() function was called.

template<int dim, int spacedim = dim>
inherited

Return a reference to the copy of the quadrature formula stored by this object.

## ◆ memory_consumption()

template<int dim, int spacedim>
 std::size_t FEFaceValuesBase< dim, spacedim >::memory_consumption ( ) const
inherited

Determine an estimate for the memory consumption (in bytes) of this object.

Definition at line 4660 of file fe_values.cc.

## ◆ shape_value()

template<int dim, int spacedim>
 const double& FEValuesBase< dim, spacedim >::shape_value ( const unsigned int function_no, const unsigned int point_no ) const
inherited

Value of a shape function at a quadrature point on the cell, face or subface selected the last time the reinit function of the derived class was called.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_value_component() function.

Parameters
 function_no Number of the shape function to be evaluated. Note that this number runs from zero to dofs_per_cell, even in the case of an FEFaceValues or FESubfaceValues object. point_no Number of the quadrature point at which function is to be evaluated
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ shape_value_component()

template<int dim, int spacedim>
 double FEValuesBase< dim, spacedim >::shape_value_component ( const unsigned int function_no, const unsigned int point_no, const unsigned int component ) const
inherited

Compute one vector component of the value of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_value() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_value() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

Parameters
 function_no Number of the shape function to be evaluated. point_no Number of the quadrature point at which function is to be evaluated. component vector component to be evaluated.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 const Tensor<1, spacedim>& FEValuesBase< dim, spacedim >::shape_grad ( const unsigned int function_no, const unsigned int quadrature_point ) const
inherited

Compute the gradient of the function_noth shape function at the quadrature_pointth quadrature point with respect to real cell coordinates. If you want to get the derivative in one of the coordinate directions, use the appropriate function of the Tensor class to extract one component of the Tensor returned by this function. Since only a reference to the gradient's value is returned, there should be no major performance drawback.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then it will throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_grad_component() function.

The same holds for the arguments of this function as for the shape_value() function.

Parameters
 function_no Number of the shape function to be evaluated. quadrature_point Number of the quadrature point at which function is to be evaluated.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 Tensor<1, spacedim> FEValuesBase< dim, spacedim >::shape_grad_component ( const unsigned int function_no, const unsigned int point_no, const unsigned int component ) const
inherited

Return one vector component of the gradient of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_grad() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_grad() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

The same holds for the arguments of this function as for the shape_value_component() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ shape_hessian()

template<int dim, int spacedim>
 const Tensor<2, spacedim>& FEValuesBase< dim, spacedim >::shape_hessian ( const unsigned int function_no, const unsigned int point_no ) const
inherited

Second derivatives of the function_noth shape function at the point_noth quadrature point with respect to real cell coordinates. If you want to get the derivatives in one of the coordinate directions, use the appropriate function of the Tensor class to extract one component. Since only a reference to the hessian values is returned, there should be no major performance drawback.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_hessian_component() function.

The same holds for the arguments of this function as for the shape_value() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ shape_hessian_component()

template<int dim, int spacedim>
 Tensor<2, spacedim> FEValuesBase< dim, spacedim >::shape_hessian_component ( const unsigned int function_no, const unsigned int point_no, const unsigned int component ) const
inherited

Return one vector component of the hessian of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_hessian() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_hessian() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

The same holds for the arguments of this function as for the shape_value_component() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ shape_3rd_derivative()

template<int dim, int spacedim>
 const Tensor<3, spacedim>& FEValuesBase< dim, spacedim >::shape_3rd_derivative ( const unsigned int function_no, const unsigned int point_no ) const
inherited

Third derivatives of the function_noth shape function at the point_noth quadrature point with respect to real cell coordinates. If you want to get the 3rd derivatives in one of the coordinate directions, use the appropriate function of the Tensor class to extract one component. Since only a reference to the 3rd derivative values is returned, there should be no major performance drawback.

If the shape function is vector-valued, then this returns the only non- zero component. If the shape function has more than one non-zero component (i.e. it is not primitive), then throw an exception of type ExcShapeFunctionNotPrimitive. In that case, use the shape_3rdderivative_component() function.

The same holds for the arguments of this function as for the shape_value() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ shape_3rd_derivative_component()

template<int dim, int spacedim>
 Tensor<3, spacedim> FEValuesBase< dim, spacedim >::shape_3rd_derivative_component ( const unsigned int function_no, const unsigned int point_no, const unsigned int component ) const
inherited

Return one vector component of the third derivative of a shape function at a quadrature point. If the finite element is scalar, then only component zero is allowed and the return value equals that of the shape_3rdderivative() function. If the finite element is vector valued but all shape functions are primitive (i.e. they are non-zero in only one component), then the value returned by shape_3rdderivative() equals that of this function for exactly one component. This function is therefore only of greater interest if the shape function is not primitive, but then it is necessary since the other function cannot be used.

The same holds for the arguments of this function as for the shape_value_component() function.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_function_values() [1/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector & fe_function, std::vector< typename InputVector::value_type > & values ) const
inherited

Return the values of a finite element function restricted to the current cell, face or subface selected the last time the reinit function of the derived class was called, at the quadrature points.

If the present cell is not active then values are interpolated to the current cell and point values are computed from that.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. To get values of multi- component elements, there is another get_function_values() below, returning a vector of vectors of results.

Parameters
 [in] fe_function A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. [out] values The values of the function specified by fe_function at the quadrature points of the current cell. The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the values of shape function times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). This happens to be equal to the type of the elements of the solution vector.
Postcondition
values[q] will contain the value of the field described by fe_function at the $$q$$th quadrature point.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3538 of file fe_values.cc.

## ◆ get_function_values() [2/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector & fe_function, std::vector< Vector< typename InputVector::value_type >> & values ) const
inherited

This function does the same as the other get_function_values(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
values[q] is a vector of values of the field described by fe_function at the $$q$$th quadrature point. The size of the vector accessed by values[q] equals the number of components of the finite element, i.e. values[q](c) returns the value of the $$c$$th vector component at the $$q$$th quadrature point.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3587 of file fe_values.cc.

## ◆ get_function_values() [3/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< typename InputVector::value_type > & values ) const
inherited

Generate function values from an arbitrary vector. This function does in essence the same as the first function of this name above, except that it does not make the assumption that the input vector corresponds to a DoFHandler that describes the unknowns of a finite element field (and for which we would then assume that fe_function.size() == dof_handler.n_dofs()). Rather, the nodal values corresponding to the current cell are elements of an otherwise arbitrary vector, and these elements are indexed by the second argument to this function. What the rest of the fe_function input argument corresponds to is of no consequence to this function.

Given this, the function above corresponds to passing fe_function as first argument to the current function, and using the local_dof_indices array that results from the following call as second argument to the current function:

cell->get_dof_indices (local_dof_indices);

Likewise, the function above is equivalent to calling

cell->get_dof_values (fe_function, local_dof_values);

and then calling the current function with local_dof_values as first argument, and an array with indices {0,...,fe.dofs_per_cell-1} as second argument.

The point of the current function is that one sometimes wants to evaluate finite element functions at quadrature points with nodal values that are not stored in a global vector – for example, one could modify these local values first, such as by applying a limiter or by ensuring that all nodal values are positive, before evaluating the finite element field that corresponds to these local values on the current cell. Another application is where one wants to postprocess the solution on a cell into a different finite element space on every cell, without actually creating a corresponding DoFHandler – in that case, all one would compute is a local representation of that postprocessed function, characterized by its nodal values; this function then allows the evaluation of that representation at quadrature points.

Parameters
 [in] fe_function A vector of nodal values. This vector can have an arbitrary size, as long as all elements index by indices can actually be accessed. [in] indices A vector of indices into fe_function. This vector must have length equal to the number of degrees of freedom on the current cell, and must identify elements in fe_function in the order in which degrees of freedom are indexed on the reference cell. [out] values A vector of values of the given finite element field, at the quadrature points on the current object.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3563 of file fe_values.cc.

## ◆ get_function_values() [4/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< Vector< typename InputVector::value_type >> & values ) const
inherited

Generate vector function values from an arbitrary vector.

This function corresponds to the previous one, just for the vector-valued case.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3615 of file fe_values.cc.

## ◆ get_function_values() [5/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_values ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, ArrayView< std::vector< typename InputVector::value_type >> values, const bool quadrature_points_fastest ) const
inherited

Generate vector function values from an arbitrary vector. This function is similar to the previous one, but the indices vector may also be a multiple of the number of dofs per cell. Then, the vectors in value should allow for the same multiple of the components of the finite element.

Depending on the value of the last argument, the outer vector of values has either the length of the quadrature rule (quadrature_points_fastest == false) or the length of components to be filled quadrature_points_fastest == true. If p is the current quadrature point number and i is the vector component of the solution desired, the access to values is values[p][i] if quadrature_points_fastest == false, and values[i][p] otherwise.

Since this function allows for fairly general combinations of argument sizes, be aware that the checks on the arguments may not detect errors.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3646 of file fe_values.cc.

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector & fe_function, std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> & gradients ) const
inherited

Compute the gradients of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's gradient instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
 [in] fe_function A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. [out] gradients The gradients of the function specified by fe_function at the quadrature points of the current cell. The gradients are computed in real space (as opposed to on the unit cell). The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the gradients of shape function times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument).
Postcondition
gradients[q] will contain the gradient of the field described by fe_function at the $$q$$th quadrature point. gradients[q][d] represents the derivative in coordinate direction $$d$$ at quadrature point $$q$$.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3679 of file fe_values.cc.

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector & fe_function, std::vector< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> & gradients ) const
inherited

This function does the same as the other get_function_gradients(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
gradients[q] is a vector of gradients of the field described by fe_function at the $$q$$th quadrature point. The size of the vector accessed by gradients[q] equals the number of components of the finite element, i.e. gradients[q][c] returns the gradient of the $$c$$th vector component at the $$q$$th quadrature point. Consequently, gradients[q][c][d] is the derivative in coordinate direction $$d$$ of the $$c$$th vector component of the vector field at quadrature point $$q$$ of the current cell.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3730 of file fe_values.cc.

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< Tensor< 1, spacedim, typename InputVector::value_type >> & gradients ) const
inherited

This function relates to the first of the get_function_gradients() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3705 of file fe_values.cc.

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_gradients ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, ArrayView< std::vector< Tensor< 1, spacedim, typename InputVector::value_type >>> gradients, const bool quadrature_points_fastest = false ) const
inherited

This function relates to the first of the get_function_gradients() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3759 of file fe_values.cc.

## ◆ get_function_hessians() [1/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector & fe_function, std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> & hessians ) const
inherited

Compute the tensor of second derivatives of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's second derivatives instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
 [in] fe_function A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. [out] hessians The Hessians of the function specified by fe_function at the quadrature points of the current cell. The Hessians are computed in real space (as opposed to on the unit cell). The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the Hessians of shape function times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument).
Postcondition
hessians[q] will contain the Hessian of the field described by fe_function at the $$q$$th quadrature point. hessians[q][i][j] represents the $$(i,j)$$th component of the matrix of second derivatives at quadrature point $$q$$.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3792 of file fe_values.cc.

## ◆ get_function_hessians() [2/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector & fe_function, std::vector< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> & hessians, const bool quadrature_points_fastest = false ) const
inherited

This function does the same as the other get_function_hessians(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
hessians[q] is a vector of Hessians of the field described by fe_function at the $$q$$th quadrature point. The size of the vector accessed by hessians[q] equals the number of components of the finite element, i.e. hessians[q][c] returns the Hessian of the $$c$$th vector component at the $$q$$th quadrature point. Consequently, hessians[q][c][i][j] is the $$(i,j)$$th component of the matrix of second derivatives of the $$c$$th vector component of the vector field at quadrature point $$q$$ of the current cell.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3843 of file fe_values.cc.

## ◆ get_function_hessians() [3/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< Tensor< 2, spacedim, typename InputVector::value_type >> & hessians ) const
inherited

This function relates to the first of the get_function_hessians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3818 of file fe_values.cc.

## ◆ get_function_hessians() [4/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_hessians ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, ArrayView< std::vector< Tensor< 2, spacedim, typename InputVector::value_type >>> hessians, const bool quadrature_points_fastest = false ) const
inherited

This function relates to the first of the get_function_hessians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3874 of file fe_values.cc.

## ◆ get_function_laplacians() [1/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector & fe_function, std::vector< typename InputVector::value_type > & laplacians ) const
inherited

Compute the (scalar) Laplacian (i.e. the trace of the tensor of second derivatives) of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's second derivatives instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
 [in] fe_function A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. [out] laplacians The Laplacians of the function specified by fe_function at the quadrature points of the current cell. The Laplacians are computed in real space (as opposed to on the unit cell). The object is assume to already have the correct size. The data type stored by this output vector must be what you get when you multiply the Laplacians of shape function times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). This happens to be equal to the type of the elements of the input vector.
Postcondition
laplacians[q] will contain the Laplacian of the field described by fe_function at the $$q$$th quadrature point.
For each component of the output vector, there holds laplacians[q]=trace(hessians[q]), where hessians would be the output of the get_function_hessians() function.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3905 of file fe_values.cc.

## ◆ get_function_laplacians() [2/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector & fe_function, std::vector< Vector< typename InputVector::value_type >> & laplacians ) const
inherited

This function does the same as the other get_function_laplacians(), but applied to multi-component (vector-valued) elements. The meaning of the arguments is as explained there.

Postcondition
laplacians[q] is a vector of Laplacians of the field described by fe_function at the $$q$$th quadrature point. The size of the vector accessed by laplacians[q] equals the number of components of the finite element, i.e. laplacians[q][c] returns the Laplacian of the $$c$$th vector component at the $$q$$th quadrature point.
For each component of the output vector, there holds laplacians[q][c]=trace(hessians[q][c]), where hessians would be the output of the get_function_hessians() function.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3954 of file fe_values.cc.

## ◆ get_function_laplacians() [3/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< typename InputVector::value_type > & laplacians ) const
inherited

This function relates to the first of the get_function_laplacians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3930 of file fe_values.cc.

## ◆ get_function_laplacians() [4/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< Vector< typename InputVector::value_type >> & laplacians ) const
inherited

This function relates to the first of the get_function_laplacians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 3981 of file fe_values.cc.

## ◆ get_function_laplacians() [5/5]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_laplacians ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< std::vector< typename InputVector::value_type >> & laplacians, const bool quadrature_points_fastest = false ) const
inherited

This function relates to the first of the get_function_laplacians() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4012 of file fe_values.cc.

## ◆ get_function_third_derivatives() [1/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector & fe_function, std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> & third_derivatives ) const
inherited

Compute the tensor of third derivatives of a finite element at the quadrature points of a cell. This function is the equivalent of the corresponding get_function_values() function (see there for more information) but evaluates the finite element field's third derivatives instead of its value.

This function may only be used if the finite element in use is a scalar one, i.e. has only one vector component. There is a corresponding function of the same name for vector-valued finite elements.

Parameters
 [in] fe_function A vector of values that describes (globally) the finite element function that this function should evaluate at the quadrature points of the current cell. [out] third_derivatives The third derivatives of the function specified by fe_function at the quadrature points of the current cell. The third derivatives are computed in real space (as opposed to on the unit cell). The object is assumed to already have the correct size. The data type stored by this output vector must be what you get when you multiply the third derivatives of shape function times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument).
Postcondition
third_derivatives[q] will contain the third derivatives of the field described by fe_function at the $$q$$th quadrature point. third_derivatives[q][i][j][k] represents the $$(i,j,k)$$th component of the 3rd order tensor of third derivatives at quadrature point $$q$$.
Note
The actual data type of the input vector may be either a Vector<T>, BlockVector<T>, or one of the PETSc or Trilinos vector wrapper classes. It represents a global vector of DoF values associated with the DoFHandler object with which this FEValues object was last initialized.
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4042 of file fe_values.cc.

## ◆ get_function_third_derivatives() [2/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector & fe_function, std::vector< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> & third_derivatives, const bool quadrature_points_fastest = false ) const
inherited

This function does the same as the other get_function_third_derivatives(), but applied to multi-component (vector- valued) elements. The meaning of the arguments is as explained there.

Postcondition
third_derivatives[q] is a vector of third derivatives of the field described by fe_function at the $$q$$th quadrature point. The size of the vector accessed by third_derivatives[q] equals the number of components of the finite element, i.e. third_derivatives[q][c] returns the third derivative of the $$c$$th vector component at the $$q$$th quadrature point. Consequently, third_derivatives[q][c][i][j][k] is the $$(i,j,k)$$th component of the tensor of third derivatives of the $$c$$th vector component of the vector field at quadrature point $$q$$ of the current cell.
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4095 of file fe_values.cc.

## ◆ get_function_third_derivatives() [3/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, std::vector< Tensor< 3, spacedim, typename InputVector::value_type >> & third_derivatives ) const
inherited

This function relates to the first of the get_function_third_derivatives() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4069 of file fe_values.cc.

## ◆ get_function_third_derivatives() [4/4]

template<int dim, int spacedim>
template<class InputVector >
 void FEValuesBase< dim, spacedim >::get_function_third_derivatives ( const InputVector & fe_function, const ArrayView< const types::global_dof_index > & indices, ArrayView< std::vector< Tensor< 3, spacedim, typename InputVector::value_type >>> third_derivatives, const bool quadrature_points_fastest = false ) const
inherited

This function relates to the first of the get_function_third_derivatives() function above in the same way as the get_function_values() with similar arguments relates to the first of the get_function_values() functions. See there for more information.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4126 of file fe_values.cc.

## ◆ dof_indices()

template<int dim, int spacedim>
 std_cxx20::ranges::iota_view FEValuesBase< dim, spacedim >::dof_indices ( ) const
inherited

Return an object that can be thought of as an array containing all indices from zero (inclusive) to dofs_per_cell (exclusive). This allows one to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q : fe_values.quadrature_point_indices())
for (const auto i : fe_values.dof_indices())
for (const auto j : fe_values.dof_indices())
cell_matrix(i,j) += ...; // Do something for DoF indices (i,j)
}

Here, we are looping over all degrees of freedom on all cells, with i and j taking on all valid indices for cell degrees of freedom, as defined by the finite element passed to fe_values.

## ◆ dof_indices_starting_at()

template<int dim, int spacedim>
 std_cxx20::ranges::iota_view FEValuesBase< dim, spacedim >::dof_indices_starting_at ( const unsigned int start_dof_index ) const
inherited

Return an object that can be thought of as an array containing all indices from start_dof_index (inclusive) to dofs_per_cell (exclusive). This allows one to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q : fe_values.quadrature_point_indices())
for (const auto i : fe_values.dof_indices())
for (const auto j : fe_values.dof_indices_starting_at(i))
cell_matrix(i,j) += ...; // Do something for DoF indices (i,j)
}

Here, we are looping over all local degrees of freedom on all cells, with i taking on all valid indices for cell degrees of freedom, as defined by the finite element passed to fe_values, and j taking on a specified subset of i's range, starting at i itself and ending at the number of cell degrees of freedom. In this way, we can construct the upper half and the diagonal of a stiffness matrix contribution (assuming it is symmetric, and that only one half of it needs to be computed), for example.

Note
If the start_dof_index is equal to the number of DoFs in the cell, then the returned index range is empty.

## ◆ dof_indices_ending_at()

template<int dim, int spacedim>
 std_cxx20::ranges::iota_view FEValuesBase< dim, spacedim >::dof_indices_ending_at ( const unsigned int end_dof_index ) const
inherited

Return an object that can be thought of as an array containing all indices from zero (inclusive) to end_dof_index (inclusive). This allows one to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q : fe_values.quadrature_point_indices())
for (const auto i : fe_values.dof_indices())
for (const auto j : fe_values.dof_indices_ending_at(i))
cell_matrix(i,j) += ...; // Do something for DoF indices (i,j)
}

Here, we are looping over all local degrees of freedom on all cells, with i taking on all valid indices for cell degrees of freedom, as defined by the finite element passed to fe_values, and j taking on a specified subset of i's range, starting at zero and ending at i itself. In this way, we can construct the lower half and the diagonal of a stiffness matrix contribution (assuming it is symmetric, and that only one half of it needs to be computed), for example.

Note
If the end_dof_index is equal to zero, then the returned index range is empty.

template<int dim, int spacedim>
 std_cxx20::ranges::iota_view FEValuesBase< dim, spacedim >::quadrature_point_indices ( ) const
inherited

Return an object that can be thought of as an array containing all indices from zero to n_quadrature_points. This allows to write code using range-based for loops of the following kind:

FEValues<dim> fe_values (...);
for (auto &cell : dof_handler.active_cell_iterators())
{
fe_values.reinit(cell);
for (const auto q_point : fe_values.quadrature_point_indices())
... do something at the quadrature point ...
}

Here, we are looping over all quadrature points on all cells, with q_point taking on all valid indices for quadrature points, as defined by the quadrature rule passed to fe_values.

deal.II and the C++11 standard

template<int dim, int spacedim>
 const Point& FEValuesBase< dim, spacedim >::quadrature_point ( const unsigned int q ) const
inherited

Position of the qth quadrature point in real space.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_quadrature_points flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_quadrature_points ( ) const
inherited

Return a reference to the vector of quadrature points in real space.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_quadrature_points flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ JxW()

template<int dim, int spacedim>
 double FEValuesBase< dim, spacedim >::JxW ( const unsigned int quadrature_point ) const
inherited

Mapped quadrature weight. If this object refers to a volume evaluation (i.e. the derived class is of type FEValues), then this is the Jacobi determinant times the weight of the *ith unit quadrature point.

For surface evaluations (i.e. classes FEFaceValues or FESubfaceValues), it is the mapped surface element times the weight of the quadrature point.

You can think of the quantity returned by this function as the volume or surface element $$dx, ds$$ in the integral that we implement here by quadrature.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_JxW_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_JxW_values()

template<int dim, int spacedim>
 const std::vector& FEValuesBase< dim, spacedim >::get_JxW_values ( ) const
inherited

Return a reference to the array holding the values returned by JxW().

## ◆ jacobian()

template<int dim, int spacedim>
 const DerivativeForm<1, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian ( const unsigned int quadrature_point ) const
inherited

Return the Jacobian of the transformation at the specified quadrature point, i.e. $$J_{ij}=dx_i/d\hat x_j$$

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_jacobians()

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobians ( ) const
inherited

Return a reference to the array holding the values returned by jacobian().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 const DerivativeForm<2, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian_grad ( const unsigned int quadrature_point ) const
inherited

Return the second derivative of the transformation from unit to real cell, i.e. the first derivative of the Jacobian, at the specified quadrature point, i.e. $$G_{ijk}=dJ_{jk}/d\hat x_i$$.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_grads flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobian_grads ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_grads().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_grads flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 const Tensor<3, spacedim>& FEValuesBase< dim, spacedim >::jacobian_pushed_forward_grad ( const unsigned int quadrature_point ) const
inherited

Return the second derivative of the transformation from unit to real cell, i.e. the first derivative of the Jacobian, at the specified quadrature point, pushed forward to the real cell coordinates, i.e. $$G_{ijk}=dJ_{iJ}/d\hat x_K (J_{jJ})^{-1} (J_{kK})^{-1}$$.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_grads flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_grads ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_pushed_forward_grads().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_grads flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ jacobian_2nd_derivative()

template<int dim, int spacedim>
 const DerivativeForm<3, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian_2nd_derivative ( const unsigned int quadrature_point ) const
inherited

Return the third derivative of the transformation from unit to real cell, i.e. the second derivative of the Jacobian, at the specified quadrature point, i.e. $$G_{ijkl}=\frac{d^2J_{ij}}{d\hat x_k d\hat x_l}$$.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_2nd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_jacobian_2nd_derivatives()

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobian_2nd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_2nd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_2nd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ jacobian_pushed_forward_2nd_derivative()

template<int dim, int spacedim>
 const Tensor<4, spacedim>& FEValuesBase< dim, spacedim >::jacobian_pushed_forward_2nd_derivative ( const unsigned int quadrature_point ) const
inherited

Return the third derivative of the transformation from unit to real cell, i.e. the second derivative of the Jacobian, at the specified quadrature point, pushed forward to the real cell coordinates, i.e. $$G_{ijkl}=\frac{d^2J_{iJ}}{d\hat x_K d\hat x_L} (J_{jJ})^{-1} (J_{kK})^{-1}(J_{lL})^{-1}$$.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_2nd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_jacobian_pushed_forward_2nd_derivatives()

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_2nd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_pushed_forward_2nd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_2nd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ jacobian_3rd_derivative()

template<int dim, int spacedim>
 const DerivativeForm<4, dim, spacedim>& FEValuesBase< dim, spacedim >::jacobian_3rd_derivative ( const unsigned int quadrature_point ) const
inherited

Return the fourth derivative of the transformation from unit to real cell, i.e. the third derivative of the Jacobian, at the specified quadrature point, i.e. $$G_{ijklm}=\frac{d^2J_{ij}}{d\hat x_k d\hat x_l d\hat x_m}$$.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_jacobian_3rd_derivatives()

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobian_3rd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_3rd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ jacobian_pushed_forward_3rd_derivative()

template<int dim, int spacedim>
 const Tensor<5, spacedim>& FEValuesBase< dim, spacedim >::jacobian_pushed_forward_3rd_derivative ( const unsigned int quadrature_point ) const
inherited

Return the fourth derivative of the transformation from unit to real cell, i.e. the third derivative of the Jacobian, at the specified quadrature point, pushed forward to the real cell coordinates, i.e. $$G_{ijklm}=\frac{d^3J_{iJ}}{d\hat x_K d\hat x_L d\hat x_M} (J_{jJ})^{-1} (J_{kK})^{-1} (J_{lL})^{-1} (J_{mM})^{-1}$$.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_3rd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_jacobian_pushed_forward_3rd_derivatives()

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_jacobian_pushed_forward_3rd_derivatives ( ) const
inherited

Return a reference to the array holding the values returned by jacobian_pushed_forward_3rd_derivatives().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_jacobian_pushed_forward_2nd_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ inverse_jacobian()

template<int dim, int spacedim>
 const DerivativeForm<1, spacedim, dim>& FEValuesBase< dim, spacedim >::inverse_jacobian ( const unsigned int quadrature_point ) const
inherited

Return the inverse Jacobian of the transformation at the specified quadrature point, i.e. $$J_{ij}=d\hat x_i/dx_j$$

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_inverse_jacobians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_inverse_jacobians()

template<int dim, int spacedim>
 const std::vector >& FEValuesBase< dim, spacedim >::get_inverse_jacobians ( ) const
inherited

Return a reference to the array holding the values returned by inverse_jacobian().

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_inverse_jacobians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ normal_vector()

template<int dim, int spacedim>
 const Tensor<1, spacedim>& FEValuesBase< dim, spacedim >::normal_vector ( const unsigned int i ) const
inherited

Return the normal vector at a quadrature point. If you call this function for a face (i.e., when using a FEFaceValues or FESubfaceValues object), then this function returns the outward normal vector to the cell at the ith quadrature point of the face.

In contrast, if you call this function for a cell of codimension one (i.e., when using a FEValues<dim,spacedim> object with spacedim>dim), then this function returns the normal vector to the cell – in other words, an approximation to the normal vector to the manifold in which the triangulation is embedded. There are of course two normal directions to a manifold in that case, and this function returns the "up" direction as induced by the numbering of the vertices.

The length of the vector is normalized to one.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_normal_vectors flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

## ◆ get_normal_vectors()

template<int dim, int spacedim>
 const std::vector< Tensor< 1, spacedim > > & FEValuesBase< dim, spacedim >::get_normal_vectors ( ) const
inherited

Return the normal vectors at all quadrature points represented by this object. See the normal_vector() function for what the normal vectors represent.

Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_normal_vectors flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.

Definition at line 4165 of file fe_values.cc.

## ◆ operator[]() [1/4]

template<int dim, int spacedim>
 const FEValuesViews::Scalar& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::Scalar & scalar ) const
inherited

Create a view of the current FEValues object that represents a particular scalar component of the possibly vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews and in particular in the Handling vector valued problems module.

## ◆ operator[]() [2/4]

template<int dim, int spacedim>
 const FEValuesViews::Vector& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::Vector & vector ) const
inherited

Create a view of the current FEValues object that represents a set of dim scalar components (i.e. a vector) of the vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews and in particular in the Handling vector valued problems module.

## ◆ operator[]() [3/4]

template<int dim, int spacedim>
 const FEValuesViews::SymmetricTensor<2, dim, spacedim>& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::SymmetricTensor< 2 > & tensor ) const
inherited

Create a view of the current FEValues object that represents a set of (dim*dim + dim)/2 scalar components (i.e. a symmetric 2nd order tensor) of the vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews and in particular in the Handling vector valued problems module.

## ◆ operator[]() [4/4]

template<int dim, int spacedim>
 const FEValuesViews::Tensor<2, dim, spacedim>& FEValuesBase< dim, spacedim >::operator[] ( const FEValuesExtractors::Tensor< 2 > & tensor ) const
inherited

Create a view of the current FEValues object that represents a set of (dim*dim) scalar components (i.e. a 2nd order tensor) of the vector-valued finite element. The concept of views is explained in the documentation of the namespace FEValuesViews and in particular in the Handling vector valued problems module.

## ◆ get_mapping()

template<int dim, int spacedim>
 const Mapping& FEValuesBase< dim, spacedim >::get_mapping ( ) const
inherited

Constant reference to the selected mapping object.

## ◆ get_fe()

template<int dim, int spacedim>
 const FiniteElement& FEValuesBase< dim, spacedim >::get_fe ( ) const
inherited

Constant reference to the selected finite element object.

## ◆ get_update_flags()

template<int dim, int spacedim>
 UpdateFlags FEValuesBase< dim, spacedim >::get_update_flags ( ) const
inherited

Return the update flags set for this object.

## ◆ get_cell()

template<int dim, int spacedim>
 const Triangulation< dim, spacedim >::cell_iterator FEValuesBase< dim, spacedim >::get_cell ( ) const
inherited

Return a triangulation iterator to the current cell.

Definition at line 4156 of file fe_values.cc.

## ◆ get_cell_similarity()

template<int dim, int spacedim>
 CellSimilarity::Similarity FEValuesBase< dim, spacedim >::get_cell_similarity ( ) const
inherited

Return the relation of the current cell to the previous cell. This allows re-use of some cell data (like local matrices for equations with constant coefficients) if the result is CellSimilarity::translation.

Definition at line 4334 of file fe_values.cc.

## ◆ invalidate_present_cell()

template<int dim, int spacedim>
 void FEValuesBase< dim, spacedim >::invalidate_present_cell ( )
protectedinherited

A function that is connected to the triangulation in order to reset the stored 'present_cell' iterator to an invalid one whenever the triangulation is changed and the iterator consequently becomes invalid.

Definition at line 4218 of file fe_values.cc.

## ◆ maybe_invalidate_previous_present_cell()

template<int dim, int spacedim>
 void FEValuesBase< dim, spacedim >::maybe_invalidate_previous_present_cell ( const typename Triangulation< dim, spacedim >::cell_iterator & cell )
protectedinherited

This function is called by the various reinit() functions in derived classes. Given the cell indicated by the argument, test whether we have to throw away the previously stored present_cell argument because it would require us to compare cells from different triangulations. In checking all this, also make sure that we have tria_listener connected to the triangulation to which we will set present_cell right after calling this function.

Definition at line 4236 of file fe_values.cc.

## ◆ compute_update_flags()

template<int dim, int spacedim>
 UpdateFlags FEValuesBase< dim, spacedim >::compute_update_flags ( const UpdateFlags update_flags ) const
protectedinherited

Initialize some update flags. Called from the initialize functions of derived classes, which are in turn called from their constructors.

Basically, this function finds out using the finite element and mapping object already stored which flags need to be set to compute everything the user wants, as expressed through the flags passed as argument.

Definition at line 4199 of file fe_values.cc.

## ◆ check_cell_similarity()

template<int dim, int spacedim>
 void FEValuesBase< dim, spacedim >::check_cell_similarity ( const typename Triangulation< dim, spacedim >::cell_iterator & cell )
inlineprotectedinherited

A function that checks whether the new cell is similar to the one previously used. Then, a significant amount of the data can be reused, e.g. the derivatives of the basis functions in real space, shape_grad.

Definition at line 4279 of file fe_values.cc.

## ◆ subscribe()

 void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

## ◆ unsubscribe()

 void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

## ◆ n_subscriptions()

 unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 301 of file subscriptor.h.

## ◆ list_subscribers() [1/2]

template<typename StreamType >
 void Subscriptor::list_subscribers ( StreamType & stream ) const
inlineinherited

List the subscribers to the input stream.

Definition at line 318 of file subscriptor.h.

## ◆ list_subscribers() [2/2]

 void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

## ◆ serialize()

template<class Archive >
 void Subscriptor::serialize ( Archive & ar, const unsigned int version )
inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 310 of file subscriptor.h.

## ◆ dimension

template<int dim, int spacedim = dim>
 const unsigned int FEFaceValues< dim, spacedim >::dimension = dim
static

Dimension in which this object operates.

Definition at line 4006 of file fe_values.h.

## ◆ space_dimension

template<int dim, int spacedim = dim>
 const unsigned int FEFaceValues< dim, spacedim >::space_dimension = spacedim
static

Definition at line 4008 of file fe_values.h.

## ◆ integral_dimension

template<int dim, int spacedim = dim>
 const unsigned int FEFaceValues< dim, spacedim >::integral_dimension = dim - 1
static

Dimension of the object over which we integrate. For the present class, this is equal to dim-1.

Definition at line 4014 of file fe_values.h.

## ◆ present_face_no

template<int dim, int spacedim = dim>
 unsigned int FEFaceValuesBase< dim, spacedim >::present_face_no
protectedinherited

Number of the face selected the last time the reinit() function was called.

Definition at line 3969 of file fe_values.h.

## ◆ present_face_index

template<int dim, int spacedim = dim>
 unsigned int FEFaceValuesBase< dim, spacedim >::present_face_index
protectedinherited

Index of the face selected the last time the reinit() function was called.

Definition at line 3975 of file fe_values.h.

template<int dim, int spacedim = dim>
 const hp::QCollection FEFaceValuesBase< dim, spacedim >::quadrature
protectedinherited

Store a copy of the quadrature formula here.

Definition at line 3980 of file fe_values.h.

template<int dim, int spacedim>
 const unsigned int FEValuesBase< dim, spacedim >::n_quadrature_points
inherited

Number of quadrature points of the current object. Its value is initialized by the value of max_n_quadrature_points and is updated, e.g., if FEFaceValues::reinit() is called for a new cell/face.

Note
The default value equals to the value of max_n_quadrature_points.

Definition at line 2186 of file fe_values.h.

template<int dim, int spacedim>
 const unsigned int FEValuesBase< dim, spacedim >::max_n_quadrature_points
inherited

Maximum number of quadrature points. This value might be different from n_quadrature_points, e.g., if a QCollection with different face quadrature rules has been passed to initialize FEFaceValues.

This is mostly useful to initialize arrays to allocate the maximum amount of memory that may be used when re-sizing later on to a the current number of quadrature points given by n_quadrature_points.

Definition at line 2197 of file fe_values.h.

## ◆ dofs_per_cell

template<int dim, int spacedim>
 const unsigned int FEValuesBase< dim, spacedim >::dofs_per_cell
inherited

Number of shape functions per cell. If we use this base class to evaluate a finite element on faces of cells, this is still the number of degrees of freedom per cell, not per face.

Definition at line 2204 of file fe_values.h.

## ◆ present_cell

template<int dim, int spacedim>
 std::unique_ptr FEValuesBase< dim, spacedim >::present_cell
protectedinherited

Store the cell selected last time the reinit() function was called. This is necessary for the get_function_* functions as well as the functions of same name in the extractor classes.

Definition at line 3590 of file fe_values.h.

## ◆ tria_listener_refinement

template<int dim, int spacedim>
 boost::signals2::connection FEValuesBase< dim, spacedim >::tria_listener_refinement
protectedinherited

A signal connection we use to ensure we get informed whenever the triangulation changes by refinement. We need to know about that because it invalidates all cell iterators and, as part of that, the 'present_cell' iterator we keep around between subsequent calls to reinit() in order to compute the cell similarity.

Definition at line 3606 of file fe_values.h.

## ◆ tria_listener_mesh_transform

template<int dim, int spacedim>
 boost::signals2::connection FEValuesBase< dim, spacedim >::tria_listener_mesh_transform
protectedinherited

A signal connection we use to ensure we get informed whenever the triangulation changes by mesh transformations. We need to know about that because it invalidates all cell iterators and, as part of that, the 'present_cell' iterator we keep around between subsequent calls to reinit() in order to compute the cell similarity.

Definition at line 3615 of file fe_values.h.

## ◆ mapping

template<int dim, int spacedim>
 const SmartPointer, FEValuesBase > FEValuesBase< dim, spacedim >::mapping
protectedinherited

A pointer to the mapping object associated with this FEValues object.

Definition at line 3642 of file fe_values.h.

## ◆ mapping_data

template<int dim, int spacedim>
 std::unique_ptr::InternalDataBase> FEValuesBase< dim, spacedim >::mapping_data
protectedinherited

A pointer to the internal data object of mapping, obtained from Mapping::get_data(), Mapping::get_face_data(), or Mapping::get_subface_data().

Definition at line 3650 of file fe_values.h.

## ◆ mapping_output

template<int dim, int spacedim>
 ::internal::FEValuesImplementation::MappingRelatedData FEValuesBase< dim, spacedim >::mapping_output
protectedinherited

An object into which the Mapping::fill_fe_values() and similar functions place their output.

Definition at line 3657 of file fe_values.h.

## ◆ fe

template<int dim, int spacedim>
 const SmartPointer, FEValuesBase > FEValuesBase< dim, spacedim >::fe
protectedinherited

A pointer to the finite element object associated with this FEValues object.

Definition at line 3666 of file fe_values.h.

## ◆ fe_data

template<int dim, int spacedim>
 std::unique_ptr::InternalDataBase> FEValuesBase< dim, spacedim >::fe_data
protectedinherited

A pointer to the internal data object of finite element, obtained from FiniteElement::get_data(), Mapping::get_face_data(), or FiniteElement::get_subface_data().

Definition at line 3674 of file fe_values.h.

## ◆ finite_element_output

template<int dim, int spacedim>
 ::internal::FEValuesImplementation::FiniteElementRelatedData FEValuesBase< dim, spacedim >::finite_element_output
protectedinherited

An object into which the FiniteElement::fill_fe_values() and similar functions place their output.

Definition at line 3682 of file fe_values.h.

## ◆ update_flags

template<int dim, int spacedim>
 UpdateFlags FEValuesBase< dim, spacedim >::update_flags
protectedinherited

Original update flags handed to the constructor of FEValues.

Definition at line 3688 of file fe_values.h.

## ◆ cell_similarity

template<int dim, int spacedim>
 CellSimilarity::Similarity FEValuesBase< dim, spacedim >::cell_similarity
protectedinherited

An enum variable that can store different states of the current cell in comparison to the previously visited cell. If wanted, additional states can be checked here and used in one of the methods used during reinit.

Definition at line 3706 of file fe_values.h.

The documentation for this class was generated from the following files: