Reference documentation for deal.II version Git 3f75665 2017-01-19 16:58:38 -0500
Public Member Functions | Protected Member Functions | Static Private Member Functions | List of all members
FE_Q_DG0< dim, spacedim > Class Template Reference

#include <deal.II/fe/fe_q_dg0.h>

Inheritance diagram for FE_Q_DG0< dim, spacedim >:
[legend]

Public Member Functions

 FE_Q_DG0 (const unsigned int p)
 
 FE_Q_DG0 (const Quadrature< 1 > &points)
 
virtual std::string get_name () const
 
virtual void interpolate (std::vector< double > &local_dofs, const std::vector< double > &values) const
 
virtual void interpolate (std::vector< double > &local_dofs, const std::vector< Vector< double > > &values, unsigned int offset=0) const
 
virtual void interpolate (std::vector< double > &local_dofs, const VectorSlice< const std::vector< std::vector< double > > > &values) const
 
virtual void get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const
 
virtual bool has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const
 
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes () const
 
- Public Member Functions inherited from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >
 FE_Q_Base (const TensorProductPolynomialsConst< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)
 
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 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
 
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
 
virtual bool hp_constraints_are_implemented () const
 
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 FiniteElementDomination::Domination compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const
 
- Public Member Functions inherited from FE_Poly< TensorProductPolynomialsConst< dim >, dim, spacedim >
 FE_Poly (const TensorProductPolynomialsConst< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)
 
unsigned int get_degree () const
 
std::vector< unsigned int > get_poly_space_numbering () const
 
std::vector< unsigned int > get_poly_space_numbering_inverse () 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
 
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
 
- 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 std::size_t memory_consumption () 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
 
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
 
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
 
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
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) 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
 
- Protected Member Functions inherited from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >
void initialize (const std::vector< Point< 1 > > &support_points_1d)
 
void initialize_constraints (const std::vector< Point< 1 > > &points)
 
void initialize_unit_support_points (const std::vector< Point< 1 > > &points)
 
void initialize_unit_face_support_points (const std::vector< Point< 1 > > &points)
 
void initialize_quad_dof_index_permutation ()
 
- Protected Member Functions inherited from FE_Poly< TensorProductPolynomialsConst< dim >, dim, spacedim >
void correct_third_derivatives (internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data, const internal::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const unsigned int n_q_points, const unsigned int dof) 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< bool > get_riaf_vector (const unsigned int degree)
 
static std::vector< unsigned int > get_dpo_vector (const unsigned int degree)
 

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 FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >
static::ExceptionBase & ExcFEQCannotHaveDegree0 ()
 
- 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 FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >
static std::vector< unsigned int > get_dpo_vector (const unsigned int degree)
 
- 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 FE_Poly< TensorProductPolynomialsConst< dim >, dim, spacedim >
TensorProductPolynomialsConst< dim > poly_space
 
- 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_Q_DG0< dim, spacedim >

Implementation of a scalar Lagrange finite element Qp+DG0 that yields the finite element space of continuous, piecewise polynomials of degree p in each coordinate direction plus the space of locally constant functions. This class is realized using tensor product polynomials based on equidistant or given support points.

The standard constructor of this class takes the degree p of this finite element. Alternatively, it can take a quadrature formula points defining the support points of the Lagrange interpolation in one coordinate direction.

For more information about the spacedim template parameter check the documentation of FiniteElement or the one of Triangulation.

For more information regarding this element see: Boffi, D., et al. "Local Mass Conservation of Stokes Finite Elements." Journal of Scientific Computing (2012): 1-18.

Implementation

The constructor creates a TensorProductPolynomials object that includes the tensor product of LagrangeEquidistant polynomials of degree p plus the locally constant function. This TensorProductPolynomialsConst object provides all values and derivatives of the shape functions. In case a quadrature rule is given, the constructor creates a TensorProductPolynomialsConst object that includes the tensor product of Lagrange polynomials with the support points from points and a locally constant function.

Furthermore the constructor fills the interface_constrains, the prolongation (embedding) and the restriction matrices.

Numbering of the degrees of freedom (DoFs)

The original ordering of the shape functions represented by the TensorProductPolynomialsConst is a tensor product numbering. However, the shape functions on a cell are renumbered beginning with the shape functions whose support points are at the vertices, then on the line, on the quads, and finally (for 3d) on the hexes. Finally there is a support point for the discontinuous shape function in the middle of the cell. To be explicit, these numberings are listed in the following:

Q1 elements

Q2 elements

Q3 elements

Q4 elements

Definition at line 237 of file fe_q_dg0.h.

Constructor & Destructor Documentation

template<int dim, int spacedim>
FE_Q_DG0< dim, spacedim >::FE_Q_DG0 ( const unsigned int  p)

Constructor for tensor product polynomials of degree p plus locally constant functions.

Definition at line 33 of file fe_q_dg0.cc.

template<int dim, int spacedim>
FE_Q_DG0< dim, spacedim >::FE_Q_DG0 ( const Quadrature< 1 > &  points)

Constructor for tensor product polynomials with support points points plus locally constant functions based on a one-dimensional quadrature formula. The degree of the finite element is points.size()-1. Note that the first point has to be 0 and the last one 1.

Definition at line 59 of file fe_q_dg0.cc.

Member Function Documentation

template<int dim, int spacedim>
std::string FE_Q_DG0< dim, spacedim >::get_name ( ) const
virtual

Return a string that uniquely identifies a finite element. This class returns FE_Q_DG0<dim>(degree), with dim and degree replaced by appropriate values.

Implements FiniteElement< dim, spacedim >.

Definition at line 89 of file fe_q_dg0.cc.

template<int dim, int spacedim>
void FE_Q_DG0< dim, spacedim >::interpolate ( std::vector< double > &  local_dofs,
const std::vector< double > &  values 
) const
virtual

Interpolate a set of scalar values, computed in the generalized support points.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 179 of file fe_q_dg0.cc.

template<int dim, int spacedim>
void FE_Q_DG0< dim, spacedim >::interpolate ( std::vector< double > &  local_dofs,
const std::vector< Vector< double > > &  values,
unsigned int  offset = 0 
) const
virtual

Interpolate a set of vector values, computed in the generalized support points.

Since a finite element often only interpolates part of a vector, offset is used to determine the first component of the vector to be interpolated. Maybe consider changing your data structures to use the next function.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 200 of file fe_q_dg0.cc.

template<int dim, int spacedim>
void FE_Q_DG0< dim, spacedim >::interpolate ( std::vector< double > &  local_dofs,
const VectorSlice< const std::vector< std::vector< double > > > &  values 
) const
virtual

Interpolate a set of vector values, computed in the generalized support points.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 227 of file fe_q_dg0.cc.

template<int dim, int spacedim>
void FE_Q_DG0< dim, spacedim >::get_interpolation_matrix ( const FiniteElement< dim, spacedim > &  source,
FullMatrix< double > &  matrix 
) const
virtual

Return the matrix interpolating from the given finite element to the present one. The size of the matrix is then dofs_per_cell times source.dofs_per_cell.

These matrices are only available if the source element is also a FE_Q_DG0 element. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >.

Definition at line 255 of file fe_q_dg0.cc.

template<int dim, int spacedim>
bool FE_Q_DG0< 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 FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >.

Definition at line 308 of file fe_q_dg0.cc.

template<int dim, int spacedim>
std::pair< Table< 2, bool >, std::vector< unsigned int > > FE_Q_DG0< dim, spacedim >::get_constant_modes ( ) const
virtual

Return a list of constant modes of the element. For this element, there are two constant modes despite the element is scalar: The first constant mode is all ones for the usual FE_Q basis and the second one only using the discontinuous part.

Reimplemented from FE_Q_Base< TensorProductPolynomialsConst< dim >, dim, spacedim >.

Definition at line 322 of file fe_q_dg0.cc.

template<int dim, int spacedim>
FiniteElement< dim, spacedim > * FE_Q_DG0< 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 170 of file fe_q_dg0.cc.

template<int dim, int spacedim>
std::vector< bool > FE_Q_DG0< dim, spacedim >::get_riaf_vector ( const unsigned int  degree)
staticprivate

Return the restriction_is_additive flags. Only the last component is true.

Definition at line 283 of file fe_q_dg0.cc.

template<int dim, int spacedim>
std::vector< unsigned int > FE_Q_DG0< 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 294 of file fe_q_dg0.cc.


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