Reference documentation for deal.II version Git f77fa7e 2014-09-22 17:58:44 +0200
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Groups Pages
Classes | Public Member Functions | Protected Member Functions | Static Private Member Functions | List of all members
FE_DGP< dim, spacedim > Class Template Reference

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

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

Classes

struct  Matrices
 

Public Member Functions

 FE_DGP (const unsigned int p)
 
virtual std::string get_name () 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
 
virtual std::pair< Table
< 2, bool >, std::vector
< unsigned int > > 
get_constant_modes () 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 FE_Poly< PolynomialSpace< dim >, dim, spacedim >
 FE_Poly (const PolynomialSpace< 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 intget_poly_space_numbering () const
 
std::vector< unsigned intget_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
 
- 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
 
 DeclException1 (ExcShapeFunctionNotPrimitive, int,<< "The shape function with index "<< arg1<< " is not primitive, i.e. it is vector-valued and "<< "has more than one non-zero vector component. This "<< "function cannot be called for these shape functions. "<< "Maybe you want to use the same function with the "<< "_component suffix?")
 
 DeclException0 (ExcFENotPrimitive)
 
 DeclException0 (ExcUnitShapeValuesDoNotExist)
 
 DeclException0 (ExcFEHasNoSupportPoints)
 
 DeclException0 (ExcEmbeddingVoid)
 
 DeclException0 (ExcProjectionVoid)
 
 DeclException0 (ExcConstraintsVoid)
 
 DeclException0 (ExcInterpolationNotImplemented)
 
 DeclException0 (ExcBoundaryFaceUsed)
 
 DeclException0 (ExcJacobiDeterminantHasWrongSign)
 
 DeclException2 (ExcWrongInterfaceMatrixSize, int, int,<< "The interface matrix has a size of "<< arg1<< "x"<< arg2<< ", which is not reasonable in the present dimension.")
 
 DeclException2 (ExcComponentIndexInvalid, int, int,<< "The component-index pair ("<< arg1<< ", "<< arg2<< ") is invalid, i.e. non-existent.")
 
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 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_index
system_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
 
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
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
- Public Member Functions inherited from FiniteElementData< dim >
 FiniteElementData ()
 
 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const unsigned int n_blocks=numbers::invalid_unsigned_int)
 
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
 
bool is_primitive () 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_Poly< PolynomialSpace< dim >, dim, spacedim >
virtual Mapping< dim, spacedim >
::InternalDataBase * 
get_data (const UpdateFlags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature) const
 
virtual void fill_fe_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Quadrature< dim > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data, CellSimilarity::Similarity &cell_similarity) const
 
virtual void fill_fe_face_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
virtual void fill_fe_subface_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
virtual UpdateFlags update_once (const UpdateFlags flags) const
 
virtual UpdateFlags update_each (const UpdateFlags flags) 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
 
void compute_2nd (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int offset, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
virtual Mapping< dim, spacedim >
::InternalDataBase * 
get_face_data (const UpdateFlags flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature) const
 
virtual Mapping< dim, spacedim >
::InternalDataBase * 
get_subface_data (const UpdateFlags flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature) const
 
- Protected Member Functions inherited from FiniteElementData< dim >
void set_primitivity (const bool value)
 

Static Private Member Functions

static std::vector< unsigned intget_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
}
 
- 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
 
BlockIndices block_indices_data
 
- Static Public Attributes inherited from FiniteElement< dim, spacedim >
static const unsigned int space_dimension
 
- 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 intcompute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)
 
- Protected Attributes inherited from FE_Poly< PolynomialSpace< dim >, dim, spacedim >
PolynomialSpace< 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< doubleinterface_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, intadjust_quad_dof_index_for_face_orientation_table
 
std::vector< intadjust_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< boolrestriction_is_additive_flags
 
const std::vector< ComponentMasknonzero_components
 
const std::vector< unsigned intn_nonzero_components_table
 
- Static Protected Attributes inherited from FiniteElement< dim, spacedim >
static const double fd_step_length
 

Detailed Description

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

Discontinuous finite elements based on Legendre polynomials.

This finite element implements complete polynomial spaces, that is, dim-dimensional polynomials of degree p. For example, in 2d the element FE_DGP(1) would represent the span of the functions \(\{1,\hat x,\hat y\}\), which is in contrast to the element FE_DGQ(1) that is formed by the span of \(\{1,\hat x,\hat y,\hat x\hat y\}\). Since the DGP space has only three unknowns for each quadrilateral, it is immediately clear that this element can not be continuous.

The basis functions used in this element for the space described above are chosen to form a Legendre basis on the unit square. As a consequence, the first basis function of this element is always the function that is constant and equal to one. As a result of the orthogonality of the basis functions, the mass matrix is diagonal if the grid cells are parallelograms. Note that this is in contrast to the FE_DGPMonomial class that actually uses the monomial basis listed above as basis functions.

The shape functions are defined in the class PolynomialSpace. The polynomials used inside PolynomialSpace are Polynomials::Legendre up to degree p given in FE_DGP. For the ordering of the basis functions, refer to PolynomialSpace, remembering that the Legendre polynomials are ordered by ascending degree.

Note
This element is not defined by finding shape functions within the given function space that interpolate a particular set of points. Consequently, there are no support points to which a given function could be interpolated; finding a finite element function that approximates a given function is therefore only possible through projection, rather than interpolation. Secondly, the shape functions of this element do not jointly add up to one. As a consequence of this, adding or subtracting a constant value – such as one would do to make a function have mean value zero – can not be done by simply subtracting the constant value from each degree of freedom. Rather, one needs to use the fact that the first basis function is constant equal to one and simply subtract the constant from the value of the degree of freedom corresponding to this first shape function on each cell.
This class is only partially implemented for the codimension one case (spacedim != dim ), since no passage of information between meshes of different refinement level is possible because the embedding and projection matrices are not computed in the class constructor.

Transformation properties

It is worth noting that under a (bi-, tri-)linear mapping, the space described by this element does not contain \(P(k)\), even if we use a basis of polynomials of degree \(k\). Consequently, for example, on meshes with non-affine cells, a linear function can not be exactly represented by elements of type FE_DGP(1) or FE_DGPMonomial(1).

This can be understood by the following 2-d example: consider the cell with vertices at \((0,0),(1,0),(0,1),(s,s)\):

dgp_doesnt_contain_p.png

For this cell, a bilinear transformation \(F\) produces the relations \(x=\hat x+\hat x\hat y\) and \(y=\hat y+\hat x\hat y\) that correlate reference coordinates \(\hat x,\hat y\) and coordinates in real space \(x,y\). Under this mapping, the constant function is clearly mapped onto itself, but the two other shape functions of the \(P_1\) space, namely \(\phi_1(\hat x,\hat y)=\hat x\) and \(\phi_2(\hat x,\hat y)=\hat y\) are mapped onto \(\phi_1(x,y)=\frac{x-t}{t(s-1)},\phi_2(x,y)=t\) where \(t=\frac{y}{s-x+sx+y-sy}\).

For the simple case that \(s=1\), i.e. if the real cell is the unit square, the expressions can be simplified to \(t=y\) and \(\phi_1(x,y)=x,\phi_2(x,y)=y\). However, for all other cases, the functions \(\phi_1(x,y),\phi_2(x,y)\) are not linear any more, and neither is any linear combincation of them. Consequently, the linear functions are not within the range of the mapped \(P_1\) polynomials.

Author
Guido Kanschat, 2001, 2002, Ralf Hartmann 2004

Definition at line 112 of file fe_dgp.h.

Constructor & Destructor Documentation

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

Constructor for tensor product polynomials of degree p.

Member Function Documentation

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

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

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
virtual std::vector<std::pair<unsigned int, unsigned int> > FE_DGP< 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 >.

template<int dim, int spacedim = dim>
virtual std::vector<std::pair<unsigned int, unsigned int> > FE_DGP< 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 >.

template<int dim, int spacedim = dim>
virtual std::vector<std::pair<unsigned int, unsigned int> > FE_DGP< 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 >.

template<int dim, int spacedim = dim>
virtual bool FE_DGP< 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_DGP 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 >.

template<int dim, int spacedim = dim>
virtual FiniteElementDomination::Domination FE_DGP< 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 FiniteElementBase::Domination and in particular the hp paper.

Reimplemented from FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
virtual void FE_DGP< 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 >.

template<int dim, int spacedim = dim>
virtual void FE_DGP< 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 >.

template<int dim, int spacedim = dim>
virtual bool FE_DGP< 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 >.

template<int dim, int spacedim = dim>
virtual std::size_t FE_DGP< 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 >.

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

Returns a list of constant modes of the element. For this element, the first entry is true, all other are false.

Reimplemented from FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
virtual FiniteElement<dim,spacedim>* FE_DGP< 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 >.

template<int dim, int spacedim = dim>
static std::vector<unsigned int> FE_DGP< 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.


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