Reference documentation for deal.II version Git 4a360c6 2017-05-26 05:30:59 +0200
Classes | Public Member Functions | Protected Member Functions | Static Private Member Functions | Private Attributes | Friends | List of all members
FE_DGPNonparametric< dim, spacedim > Class Template Reference

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

Inheritance diagram for FE_DGPNonparametric< dim, spacedim >:
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Classes

struct  Matrices
 

Public Member Functions

 FE_DGPNonparametric (const unsigned int k)
 
virtual std::string get_name () const
 
virtual UpdateFlags requires_update_flags (const UpdateFlags update_flags) const
 
virtual double shape_value (const unsigned int i, const Point< dim > &p) const
 
virtual double shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const
 
virtual Tensor< 1, dim > shape_grad (const unsigned int i, const Point< dim > &p) const
 
virtual Tensor< 1, dim > shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const
 
virtual Tensor< 2, dim > shape_grad_grad (const unsigned int i, const Point< dim > &p) const
 
virtual Tensor< 2, dim > shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const
 
unsigned int get_degree () const
 
virtual void get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const
 
virtual void get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix) const
 
virtual bool has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const
 
virtual std::size_t memory_consumption () const
 
Functions to support hp
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_vertex_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const
 
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_line_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const
 
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_quad_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const
 
virtual bool hp_constraints_are_implemented () const
 
virtual FiniteElementDomination::Domination compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const
 
- Public Member Functions inherited from FiniteElement< dim, spacedim >
 FiniteElement (const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)
 
virtual ~FiniteElement ()
 
const FiniteElement< dim, spacedim > & operator[] (const unsigned int fe_index) const
 
bool operator== (const FiniteElement< dim, spacedim > &) const
 
virtual Tensor< 3, dim > shape_3rd_derivative (const unsigned int i, const Point< dim > &p) const
 
virtual Tensor< 3, dim > shape_3rd_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const
 
virtual Tensor< 4, dim > shape_4th_derivative (const unsigned int i, const Point< dim > &p) const
 
virtual Tensor< 4, dim > shape_4th_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const
 
virtual const FullMatrix< double > & get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const
 
virtual const FullMatrix< double > & get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const
 
bool prolongation_is_implemented () const
 
bool isotropic_prolongation_is_implemented () const
 
bool restriction_is_implemented () const
 
bool isotropic_restriction_is_implemented () const
 
bool restriction_is_additive (const unsigned int index) const
 
const FullMatrix< double > & constraints (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const
 
bool constraints_are_implemented (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const
 
virtual void get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const
 
std::pair< unsigned int, unsigned int > system_to_component_index (const unsigned int index) const
 
unsigned int component_to_system_index (const unsigned int component, const unsigned int index) const
 
std::pair< unsigned int, unsigned int > face_system_to_component_index (const unsigned int index) const
 
unsigned int adjust_quad_dof_index_for_face_orientation (const unsigned int index, const bool face_orientation, const bool face_flip, const bool face_rotation) const
 
virtual unsigned int face_to_cell_index (const unsigned int face_dof_index, const unsigned int face, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false) const
 
unsigned int adjust_line_dof_index_for_line_orientation (const unsigned int index, const bool line_orientation) const
 
const ComponentMaskget_nonzero_components (const unsigned int i) const
 
unsigned int n_nonzero_components (const unsigned int i) const
 
bool is_primitive () const
 
bool is_primitive (const unsigned int i) const
 
unsigned int n_base_elements () const
 
virtual const FiniteElement< dim, spacedim > & base_element (const unsigned int index) const
 
unsigned int element_multiplicity (const unsigned int index) const
 
std::pair< std::pair< unsigned int, unsigned int >, unsigned int > system_to_base_index (const unsigned int index) const
 
std::pair< std::pair< unsigned int, unsigned int >, unsigned int > face_system_to_base_index (const unsigned int index) const
 
types::global_dof_index first_block_of_base (const unsigned int b) const
 
std::pair< unsigned int, unsigned int > component_to_base_index (const unsigned int component) const
 
std::pair< unsigned int, unsigned int > block_to_base_index (const unsigned int block) const
 
std::pair< unsigned int, types::global_dof_indexsystem_to_block_index (const unsigned int component) const
 
unsigned int component_to_block_index (const unsigned int component) const
 
ComponentMask component_mask (const FEValuesExtractors::Scalar &scalar) const
 
ComponentMask component_mask (const FEValuesExtractors::Vector &vector) const
 
ComponentMask component_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const
 
ComponentMask component_mask (const BlockMask &block_mask) const
 
BlockMask block_mask (const FEValuesExtractors::Scalar &scalar) const
 
BlockMask block_mask (const FEValuesExtractors::Vector &vector) const
 
BlockMask block_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const
 
BlockMask block_mask (const ComponentMask &component_mask) const
 
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes () const
 
const std::vector< Point< dim > > & get_unit_support_points () const
 
bool has_support_points () const
 
virtual Point< dim > unit_support_point (const unsigned int index) const
 
const std::vector< Point< dim-1 > > & get_unit_face_support_points () const
 
bool has_face_support_points () const
 
virtual Point< dim-1 > unit_face_support_point (const unsigned int index) const
 
const std::vector< Point< dim > > & get_generalized_support_points () const
 
bool has_generalized_support_points () const
 
const std::vector< Point< dim-1 > > & get_generalized_face_support_points () const
 
bool has_generalized_face_support_points () const
 
GeometryPrimitive get_associated_geometry_primitive (const unsigned int cell_dof_index) const
 
virtual void convert_generalized_support_point_values_to_nodal_values (const std::vector< Vector< double > > &support_point_values, std::vector< double > &nodal_values) const
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=nullptr) const
 
void unsubscribe (const char *identifier=nullptr) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
- Public Member Functions inherited from FiniteElementData< dim >
 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices())
 
unsigned int n_dofs_per_vertex () const
 
unsigned int n_dofs_per_line () const
 
unsigned int n_dofs_per_quad () const
 
unsigned int n_dofs_per_hex () const
 
unsigned int n_dofs_per_face () const
 
unsigned int n_dofs_per_cell () const
 
template<int structdim>
unsigned int n_dofs_per_object () const
 
unsigned int n_components () const
 
unsigned int n_blocks () const
 
const BlockIndicesblock_indices () const
 
unsigned int tensor_degree () const
 
bool conforms (const Conformity) const
 
bool operator== (const FiniteElementData &) const
 

Protected Member Functions

virtual FiniteElement< dim, spacedim > * clone () const
 
virtual FiniteElement< dim, spacedim >::InternalDataBaseget_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature,::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const
 
- Protected Member Functions inherited from FiniteElement< dim, spacedim >
void reinit_restriction_and_prolongation_matrices (const bool isotropic_restriction_only=false, const bool isotropic_prolongation_only=false)
 
TableIndices< 2 > interface_constraints_size () const
 
virtual InternalDataBaseget_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature,::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const
 
virtual InternalDataBaseget_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature,::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const
 
virtual void fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal,::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const =0
 
virtual void fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal,::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const =0
 
virtual void fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal,::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const =0
 

Static Private Member Functions

static std::vector< unsigned int > get_dpo_vector (const unsigned int degree)
 

Private Attributes

const PolynomialSpace< dim > polynomial_space
 

Friends

template<int , int >
class FE_DGPNonparametric
 

Additional Inherited Members

- Public Types inherited from FiniteElementData< dim >
enum  Conformity {
  unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04,
  H1 = Hcurl | Hdiv, H2 = 0x0e
}
 
- Static Public Member Functions inherited from FiniteElement< dim, spacedim >
static::ExceptionBase & ExcShapeFunctionNotPrimitive (int arg1)
 
static::ExceptionBase & ExcFENotPrimitive ()
 
static::ExceptionBase & ExcUnitShapeValuesDoNotExist ()
 
static::ExceptionBase & ExcFEHasNoSupportPoints ()
 
static::ExceptionBase & ExcEmbeddingVoid ()
 
static::ExceptionBase & ExcProjectionVoid ()
 
static::ExceptionBase & ExcWrongInterfaceMatrixSize (int arg1, int arg2)
 
static::ExceptionBase & ExcInterpolationNotImplemented ()
 
- Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 
- Public Attributes inherited from FiniteElementData< dim >
const unsigned int dofs_per_vertex
 
const unsigned int dofs_per_line
 
const unsigned int dofs_per_quad
 
const unsigned int dofs_per_hex
 
const unsigned int first_line_index
 
const unsigned int first_quad_index
 
const unsigned int first_hex_index
 
const unsigned int first_face_line_index
 
const unsigned int first_face_quad_index
 
const unsigned int dofs_per_face
 
const unsigned int dofs_per_cell
 
const unsigned int components
 
const unsigned int degree
 
const Conformity conforming_space
 
const BlockIndices block_indices_data
 
- Static Public Attributes inherited from FiniteElement< dim, spacedim >
static const unsigned int space_dimension = spacedim
 
- Static Public Attributes inherited from FiniteElementData< dim >
static const unsigned int dimension = dim
 
- Static Protected Member Functions inherited from FiniteElement< dim, spacedim >
static std::vector< unsigned int > compute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)
 
- Protected Attributes inherited from FiniteElement< dim, spacedim >
std::vector< std::vector< FullMatrix< double > > > restriction
 
std::vector< std::vector< FullMatrix< double > > > prolongation
 
FullMatrix< double > interface_constraints
 
std::vector< Point< dim > > unit_support_points
 
std::vector< Point< dim-1 > > unit_face_support_points
 
std::vector< Point< dim > > generalized_support_points
 
std::vector< Point< dim-1 > > generalized_face_support_points
 
Table< 2, int > adjust_quad_dof_index_for_face_orientation_table
 
std::vector< int > adjust_line_dof_index_for_line_orientation_table
 
std::vector< std::pair< unsigned int, unsigned int > > system_to_component_table
 
std::vector< std::pair< unsigned int, unsigned int > > face_system_to_component_table
 
std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > system_to_base_table
 
std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > face_system_to_base_table
 
BlockIndices base_to_block_indices
 
std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > component_to_base_table
 
const std::vector< bool > restriction_is_additive_flags
 
const std::vector< ComponentMasknonzero_components
 
const std::vector< unsigned int > n_nonzero_components_table
 
const bool cached_primitivity
 

Detailed Description

template<int dim, int spacedim = dim>
class FE_DGPNonparametric< dim, spacedim >

Discontinuous finite elements evaluated at the mapped quadrature points.

Warning: this class does not work properly, yet. Don't use it!

This finite element implements complete polynomial spaces, that is, \(d\)-dimensional polynomials of order \(k\).

The polynomials are not mapped. Therefore, they are constant, linear, quadratic, etc. on any grid cell.

Since the polynomials are evaluated at the quadrature points of the actual grid cell, no grid transfer and interpolation matrices are available.

The purpose of this class is experimental, therefore the implementation will remain incomplete.

Besides, this class is not implemented for the codimension one case (spacedim != dim).

Visualization of shape functions

In 2d, the shape functions of this element look as follows.

\(P_0\) element

P1_DGPNonparametric_shape0000.png

\(P_0\) element, shape function 0

\(P_1\) element

P1_DGPNonparametric_shape0000.png

P1_DGPNonparametric_shape0001.png

\(P_1\) element, shape function 0

\(P_1\) element, shape function 1

P1_DGPNonparametric_shape0002.png

\(P_1\) element, shape function 2

\(P_2\) element

P2_DGPNonparametric_shape0000.png

P2_DGPNonparametric_shape0001.png

\(P_2\) element, shape function 0

\(P_2\) element, shape function 1

P2_DGPNonparametric_shape0002.png

P2_DGPNonparametric_shape0003.png

\(P_2\) element, shape function 2

\(P_2\) element, shape function 3

P2_DGPNonparametric_shape0004.png

P2_DGPNonparametric_shape0005.png

\(P_2\) element, shape function 4

\(P_2\) element, shape function 5

\(P_3\) element

P3_DGPNonparametric_shape0000.png

P3_DGPNonparametric_shape0001.png

\(P_3\) element, shape function 0

\(P_3\) element, shape function 1

P3_DGPNonparametric_shape0002.png

P3_DGPNonparametric_shape0003.png

\(P_3\) element, shape function 2

\(P_3\) element, shape function 3

P3_DGPNonparametric_shape0004.png

P3_DGPNonparametric_shape0005.png

\(P_3\) element, shape function 4

\(P_3\) element, shape function 5

P3_DGPNonparametric_shape0006.png

P3_DGPNonparametric_shape0007.png

\(P_3\) element, shape function 6

\(P_3\) element, shape function 7

P3_DGPNonparametric_shape0008.png

P3_DGPNonparametric_shape0009.png

\(P_3\) element, shape function 8

\(P_3\) element, shape function 9

\(P_4\) element

P4_DGPNonparametric_shape0000.png

P4_DGPNonparametric_shape0001.png

\(P_4\) element, shape function 0

\(P_4\) element, shape function 1

P4_DGPNonparametric_shape0002.png

P4_DGPNonparametric_shape0003.png

\(P_4\) element, shape function 2

\(P_4\) element, shape function 3

P4_DGPNonparametric_shape0004.png

P4_DGPNonparametric_shape0005.png

\(P_4\) element, shape function 4

\(P_4\) element, shape function 5

P4_DGPNonparametric_shape0006.png

P4_DGPNonparametric_shape0007.png

\(P_4\) element, shape function 6

\(P_4\) element, shape function 7

P4_DGPNonparametric_shape0008.png

P4_DGPNonparametric_shape0009.png

\(P_4\) element, shape function 8

\(P_4\) element, shape function 9

P4_DGPNonparametric_shape0010.png

P4_DGPNonparametric_shape0011.png

\(P_4\) element, shape function 10

\(P_4\) element, shape function 11

P4_DGPNonparametric_shape0012.png

P4_DGPNonparametric_shape0013.png

\(P_4\) element, shape function 12

\(P_4\) element, shape function 13

P4_DGPNonparametric_shape0014.png

\(P_4\) element, shape function 14

Implementation details

This element does not have an InternalData class, unlike all other elements, because the InternalData classes are used to store things that can be computed once and reused multiple times (such as the values of shape functions at quadrature points on the reference cell). However, because the element is not mapped, this element has nothing that could be computed on the reference cell – everything needs to be computed on the real cell – and consequently there is nothing we'd like to store in such an object. We can thus simply use the members already provided by FiniteElement::InternalDataBase without adding anything in a derived class in this class.

Author
Guido Kanschat, 2002

Definition at line 269 of file fe_dgp_nonparametric.h.

Constructor & Destructor Documentation

template<int dim, int spacedim>
FE_DGPNonparametric< dim, spacedim >::FE_DGPNonparametric ( const unsigned int  k)

Constructor for tensor product polynomials of degree k.

Definition at line 31 of file fe_dgp_nonparametric.cc.

Member Function Documentation

template<int dim, int spacedim>
std::string FE_DGPNonparametric< dim, spacedim >::get_name ( ) const
virtual

Return a string that uniquely identifies a finite element. This class returns FE_DGPNonparametric<dim>(degree), with dim and degree replaced by appropriate values.

Implements FiniteElement< dim, spacedim >.

Definition at line 97 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
UpdateFlags FE_DGPNonparametric< dim, spacedim >::requires_update_flags ( const UpdateFlags  update_flags) const
virtual

Given a set of update flags, compute which other quantities also need to be computed in order to satisfy the request by the given flags. Then return the combination of the original set of flags and those just computed.

As an example, if update_flags contains update_gradients a finite element class will typically require the computation of the inverse of the Jacobian matrix in order to rotate the gradient of shape functions on the reference cell to the real cell. It would then return not just update_gradients, but also update_covariant_transformation, the flag that makes the mapping class produce the inverse of the Jacobian matrix.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

See also
UpdateFlags

Implements FiniteElement< dim, spacedim >.

Definition at line 239 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
double FE_DGPNonparametric< dim, spacedim >::shape_value ( const unsigned int  i,
const Point< dim > &  p 
) const
virtual

This function is intended to return the value of a shape function at a point on the reference cell. However, since the current element does not implement shape functions by mapping from a reference cell, no shape functions exist on the reference cell.

Consequently, as discussed in the corresponding function in the base class, FiniteElement::shape_value(), this function throws an exception of type FiniteElement::ExcUnitShapeValuesDoNotExist.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 127 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
double FE_DGPNonparametric< dim, spacedim >::shape_value_component ( const unsigned int  i,
const Point< dim > &  p,
const unsigned int  component 
) const
virtual

This function is intended to return the value of a shape function at a point on the reference cell. However, since the current element does not implement shape functions by mapping from a reference cell, no shape functions exist on the reference cell.

Consequently, as discussed in the corresponding function in the base class, FiniteElement::shape_value_component(), this function throws an exception of type FiniteElement::ExcUnitShapeValuesDoNotExist.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 141 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
Tensor< 1, dim > FE_DGPNonparametric< dim, spacedim >::shape_grad ( const unsigned int  i,
const Point< dim > &  p 
) const
virtual

This function is intended to return the gradient of a shape function at a point on the reference cell. However, since the current element does not implement shape functions by mapping from a reference cell, no shape functions exist on the reference cell.

Consequently, as discussed in the corresponding function in the base class, FiniteElement::shape_grad(), this function throws an exception of type FiniteElement::ExcUnitShapeValuesDoNotExist.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 158 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
Tensor< 1, dim > FE_DGPNonparametric< dim, spacedim >::shape_grad_component ( const unsigned int  i,
const Point< dim > &  p,
const unsigned int  component 
) const
virtual

This function is intended to return the gradient of a shape function at a point on the reference cell. However, since the current element does not implement shape functions by mapping from a reference cell, no shape functions exist on the reference cell.

Consequently, as discussed in the corresponding function in the base class, FiniteElement::shape_grad_component(), this function throws an exception of type FiniteElement::ExcUnitShapeValuesDoNotExist.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 171 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
Tensor< 2, dim > FE_DGPNonparametric< dim, spacedim >::shape_grad_grad ( const unsigned int  i,
const Point< dim > &  p 
) const
virtual

This function is intended to return the Hessian of a shape function at a point on the reference cell. However, since the current element does not implement shape functions by mapping from a reference cell, no shape functions exist on the reference cell.

Consequently, as discussed in the corresponding function in the base class, FiniteElement::shape_grad_grad(), this function throws an exception of type FiniteElement::ExcUnitShapeValuesDoNotExist.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 188 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
Tensor< 2, dim > FE_DGPNonparametric< dim, spacedim >::shape_grad_grad_component ( const unsigned int  i,
const Point< dim > &  p,
const unsigned int  component 
) const
virtual

This function is intended to return the Hessian of a shape function at a point on the reference cell. However, since the current element does not implement shape functions by mapping from a reference cell, no shape functions exist on the reference cell.

Consequently, as discussed in the corresponding function in the base class, FiniteElement::shape_grad_grad_component(), this function throws an exception of type FiniteElement::ExcUnitShapeValuesDoNotExist.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 202 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
unsigned int FE_DGPNonparametric< dim, spacedim >::get_degree ( ) const

Return the polynomial degree of this finite element, i.e. the value passed to the constructor.

Definition at line 585 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
void FE_DGPNonparametric< dim, spacedim >::get_face_interpolation_matrix ( const FiniteElement< dim, spacedim > &  source,
FullMatrix< double > &  matrix 
) const
virtual

Return the matrix interpolating from a face of of one element to the face of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Derived elements will have to implement this function. They may only provide interpolation matrices for certain source finite elements, for example those from the same family. If they don't implement interpolation from a given element, then they must throw an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 422 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
void FE_DGPNonparametric< dim, spacedim >::get_subface_interpolation_matrix ( const FiniteElement< dim, spacedim > &  source,
const unsigned int  subface,
FullMatrix< double > &  matrix 
) const
virtual

Return the matrix interpolating from a face of of one element to the face of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Derived elements will have to implement this function. They may only provide interpolation matrices for certain source finite elements, for example those from the same family. If they don't implement interpolation from a given element, then they must throw an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 452 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
std::vector< std::pair< unsigned int, unsigned int > > FE_DGPNonparametric< dim, spacedim >::hp_vertex_dof_identities ( const FiniteElement< dim, spacedim > &  fe_other) const
virtual

If, on a vertex, several finite elements are active, the hp code first assigns the degrees of freedom of each of these FEs different global indices. It then calls this function to find out which of them should get identical values, and consequently can receive the same global DoF index. This function therefore returns a list of identities between DoFs of the present finite element object with the DoFs of fe_other, which is a reference to a finite element object representing one of the other finite elements active on this particular vertex. The function computes which of the degrees of freedom of the two finite element objects are equivalent, both numbered between zero and the corresponding value of dofs_per_vertex of the two finite elements. The first index of each pair denotes one of the vertex dofs of the present element, whereas the second is the corresponding index of the other finite element.

This being a discontinuous element, the set of such constraints is of course empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 492 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
std::vector< std::pair< unsigned int, unsigned int > > FE_DGPNonparametric< dim, spacedim >::hp_line_dof_identities ( const FiniteElement< dim, spacedim > &  fe_other) const
virtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.

This being a discontinuous element, the set of such constraints is of course empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 511 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
std::vector< std::pair< unsigned int, unsigned int > > FE_DGPNonparametric< dim, spacedim >::hp_quad_dof_identities ( const FiniteElement< dim, spacedim > &  fe_other) const
virtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.

This being a discontinuous element, the set of such constraints is of course empty.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 530 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
bool FE_DGPNonparametric< dim, spacedim >::hp_constraints_are_implemented ( ) const
virtual

Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp compatible".

For the FE_DGPNonparametric class the result is always true (independent of the degree of the element), as it has no hanging nodes (being a discontinuous element).

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 482 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
FiniteElementDomination::Domination FE_DGPNonparametric< dim, spacedim >::compare_for_face_domination ( const FiniteElement< dim, spacedim > &  fe_other) const
virtual

Return whether this element dominates the one given as argument when they meet at a common face, whether it is the other way around, whether neither dominates, or if either could dominate.

For a definition of domination, see FiniteElementDomination::Domination and in particular the hp paper.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 549 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
bool FE_DGPNonparametric< dim, spacedim >::has_support_on_face ( const unsigned int  shape_index,
const unsigned int  face_index 
) const
virtual

This function returns true, if the shape function shape_index has non-zero function values somewhere on the face face_index.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 565 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
std::size_t FE_DGPNonparametric< dim, spacedim >::memory_consumption ( ) const
virtual

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

This function is made virtual, since finite element objects are usually accessed through pointers to their base class, rather than the class itself.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 575 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
FiniteElement< dim, spacedim > * FE_DGPNonparametric< dim, spacedim >::clone ( ) const
protectedvirtual

clone function instead of a copy constructor.

This function is needed by the constructors of FESystem.

Implements FiniteElement< dim, spacedim >.

Definition at line 118 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
FiniteElement< dim, spacedim >::InternalDataBase * FE_DGPNonparametric< dim, spacedim >::get_data ( const UpdateFlags  update_flags,
const Mapping< dim, spacedim > &  mapping,
const Quadrature< dim > &  quadrature,
::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &  output_data 
) const
protectedvirtual

Prepare internal data structures and fill in values independent of the cell.

Implements FiniteElement< dim, spacedim >.

Definition at line 258 of file fe_dgp_nonparametric.cc.

template<int dim, int spacedim>
std::vector< unsigned int > FE_DGPNonparametric< dim, spacedim >::get_dpo_vector ( const unsigned int  degree)
staticprivate

Only for internal use. Its full name is get_dofs_per_object_vector function and it creates the dofs_per_object vector that is needed within the constructor to be passed to the constructor of FiniteElementData.

Definition at line 223 of file fe_dgp_nonparametric.cc.

Friends And Related Function Documentation

template<int dim, int spacedim = dim>
template<int , int >
friend class FE_DGPNonparametric
friend

Allow access from other dimensions.

Definition at line 608 of file fe_dgp_nonparametric.h.

Member Data Documentation

template<int dim, int spacedim = dim>
const PolynomialSpace<dim> FE_DGPNonparametric< dim, spacedim >::polynomial_space
private

Pointer to an object representing the polynomial space used here.

Definition at line 603 of file fe_dgp_nonparametric.h.


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