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

Inheritance diagram for FE_Q_Bubbles< dim, spacedim >:

Public Member Functions
	FE_Q_Bubbles (const unsigned int p)

	FE_Q_Bubbles (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 const FullMatrix< double > &	get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case) const

virtual const FullMatrix< double > &	get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case) const

virtual bool	has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const

Public Member Functions inherited from FE_Q_Base< TensorProductPolynomialsBubbles< dim >, dim, spacedim >
	FE_Q_Base (const TensorProductPolynomialsBubbles< 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 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 std::pair< Table< 2, bool >, std::vector< unsigned int > >	get_constant_modes () 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< TensorProductPolynomialsBubbles< dim >, dim, spacedim >
	FE_Poly (const TensorProductPolynomialsBubbles< 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

	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)

	DeclExceptionMsg (ExcUnitShapeValuesDoNotExist, "You are trying to access the values or derivatives of shape functions " "on the reference cell of an element that does not define its shape " "functions through mapping from the reference cell. Consequently, " "you cannot ask for shape function values or derivatives on the " "reference cell.")

	DeclExceptionMsg (ExcFEHasNoSupportPoints, "You are trying to access the support points of a finite " "element that either has no support points at all, or for " "which the corresponding tables have not been implemented.")

	DeclExceptionMsg (ExcEmbeddingVoid, "You are trying to access the matrices that describe how " "to embed a finite element function on one cell into the " "finite element space on one of its children (i.e., the " "'embedding' or 'prolongation' matrices). However, the " "current finite element can either not define this sort of " "operation, or it has not yet been implemented.")

	DeclExceptionMsg (ExcProjectionVoid, "You are trying to access the matrices that describe how " "to restrict a finite element function from the children " "of one cell to the finite element space defined on their " "parent (i.e., the 'restriction' or 'projection' matrices). " "However, the current finite element can either not define " "this sort of operation, or it has not yet been " "implemented.")

	DeclException2 (ExcWrongInterfaceMatrixSize, int, int,<< "The interface matrix has a size of "<< arg1<< "x"<< arg2<< ", which is not reasonable for the current element " "in the present dimension.")

	DeclException0 (ExcInterpolationNotImplemented)

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 ComponentMask &	get_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

GeometryPrimitive	get_associated_geometry_primitive (const unsigned int cell_dof_index) const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

virtual	~Subscriptor ()

Subscriptor &	operator= (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."<< "\"<< "(Additional information: "<< arg3<< ")\"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")

	DeclException2 (ExcNoSubscriber, char , char ,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")

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 BlockIndices &	block_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_Q_Base< TensorProductPolynomialsBubbles< 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< TensorProductPolynomialsBubbles< 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 InternalDataBase *	get_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 InternalDataBase *	get_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

Protected Member Functions inherited from FiniteElementData< dim >
void	set_primitivity (const bool value)

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)

Private Attributes
const unsigned int	n_bubbles

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

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< TensorProductPolynomialsBubbles< 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< TensorProductPolynomialsBubbles< dim >, dim, spacedim >
TensorProductPolynomialsBubbles< 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< ComponentMask >	nonzero_components

const std::vector< unsigned int >	n_nonzero_components_table

Detailed Description

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

Implementation of a scalar Lagrange finite element Q_p^+ that yields the finite element space of continuous, piecewise polynomials of degree p in each coordinate direction plus some bubble enrichment space spanned by $(2x_j-1)^{p-1}\prod_{i=0}^{dim-1}(x_i(1-x_i))$ . Therefore the highest polynomial degree is $p+1$ . 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.

Due to the fact that the enrichments are small almost everywhere for large p, the condition number for the mass and stiffness matrix fastly increaseses with increasing p. Below you see a comparison with FE_Q(QGaussLobatto(p+1)) for dim=1.

Therefore, this element should be used with care for $p>3$ .

Implementation

The constructor creates a TensorProductPolynomials object that includes the tensor product of LagrangeEquidistant polynomials of degree p plus the bubble enrichments. This TensorProductPolynomialsBubbles object provides all values and derivatives of the shape functions. In case a quadrature rule is given, the constructor creates a TensorProductPolynomialsBubbles object that includes the tensor product of Lagrange polynomials with the support points from points and the bubble enrichments as defined above.

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 TensorProductPolynomialsBubbles 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 are support points for the bubble enrichments in the middle of the cell.

Definition at line 83 of file fe_q_bubbles.h.

Constructor & Destructor Documentation

§ FE_Q_Bubbles() [1/2]

template<int dim, int spacedim>

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

Constructor for tensor product polynomials of degree p plus bubble enrichments

Definition at line 172 of file fe_q_bubbles.cc.

§ FE_Q_Bubbles() [2/2]

template<int dim, int spacedim>

FE_Q_Bubbles< dim, spacedim >::FE_Q_Bubbles ( const Quadrature< 1 > & points )

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

Definition at line 214 of file fe_q_bubbles.cc.

Member Function Documentation

§ get_name()

template<int dim, int spacedim>

std::string FE_Q_Bubbles< dim, spacedim >::get_name ( ) const

virtual

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

Implements FiniteElement< dim, spacedim >.

Definition at line 254 of file fe_q_bubbles.cc.

§ interpolate() [1/3]

template<int dim, int spacedim>

void FE_Q_Bubbles< 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 331 of file fe_q_bubbles.cc.

§ interpolate() [2/3]

template<int dim, int spacedim>

void FE_Q_Bubbles< 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 353 of file fe_q_bubbles.cc.

§ interpolate() [3/3]

template<int dim, int spacedim>

void FE_Q_Bubbles< 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 381 of file fe_q_bubbles.cc.

§ get_interpolation_matrix()

template<int dim, int spacedim>

void FE_Q_Bubbles< 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_Bubbles element. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

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

Definition at line 410 of file fe_q_bubbles.cc.

§ get_prolongation_matrix()

template<int dim, int spacedim>

const FullMatrix< double > & FE_Q_Bubbles< dim, spacedim >::get_prolongation_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case
	)		const

virtual

Embedding matrix between grids. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when queried).

The identity operator from a coarse grid space into a fine grid space is associated with a matrix P. The restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation, not the sum of the cell matrices P_i. That is, if the same non-zero entry j,k exists in in two different child matrices P_i, the value should be the same in both matrices and it is copied into the matrix P only once.

Row and column indices are related to fine grid and coarse grid spaces, respectively, consistent with the definition of the associated operator.

These matrices are used by routines assembling the prolongation matrix for multi-level methods. Upon assembling the transfer matrix between cells using this matrix array, zero elements in the prolongation matrix are discarded and will not fill up the transfer matrix.

If projection matrices are not implemented in the derived finite element class, this function aborts with ExcEmbeddingVoid. You can check whether this is the case by calling the prolongation_is_implemented() or the isotropic_prolongation_is_implemented() function.

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

Definition at line 486 of file fe_q_bubbles.cc.

§ get_restriction_matrix()

template<int dim, int spacedim>

const FullMatrix< double > & FE_Q_Bubbles< dim, spacedim >::get_restriction_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case
	)		const

virtual

Projection from a fine grid space onto a coarse grid space. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when requested).

If this projection operator is associated with a matrix P, then the restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation or the sum of the cell matrices P_i, depending on the restriction_is_additive_flags. This distinguishes interpolation (concatenation) and projection with respect to scalar products (summation).

Row and column indices are related to coarse grid and fine grid spaces, respectively, consistent with the definition of the associated operator.

If projection matrices are not implemented in the derived finite element class, this function aborts with ExcProjectionVoid. You can check whether this is the case by calling the restriction_is_implemented() or the isotropic_restriction_is_implemented() function.

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

Definition at line 507 of file fe_q_bubbles.cc.

§ has_support_on_face()

template<int dim, int spacedim>

bool FE_Q_Bubbles< dim, spacedim >::has_support_on_face	(	const unsigned int	shape_index,
		const unsigned int	face_index
	)		const

virtual

Check for non-zero values on a face.

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

Implementation of the interface in FiniteElement

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

Definition at line 471 of file fe_q_bubbles.cc.

§ clone()

template<int dim, int spacedim>

FiniteElement< dim, spacedim > * FE_Q_Bubbles< 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 322 of file fe_q_bubbles.cc.

§ get_riaf_vector()

template<int dim, int spacedim>

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

staticprivate

Returns the restriction_is_additive flags. Only the last components for the bubble enrichments are true.

Definition at line 445 of file fe_q_bubbles.cc.

§ get_dpo_vector()

template<int dim, int spacedim>

std::vector< unsigned int > FE_Q_Bubbles< 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 456 of file fe_q_bubbles.cc.

Member Data Documentation

§ n_bubbles

template<int dim, int spacedim = dim>

const unsigned int FE_Q_Bubbles< dim, spacedim >::n_bubbles

private

Number of additional bubble functions

Definition at line 195 of file fe_q_bubbles.h.

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

deal.II/fe/fe_q_bubbles.h
/build/deal.ii-pdtiAo/deal.ii-8.4.2/source/fe/fe_q_bubbles.cc

Public Member Functions

Protected Member Functions

Static Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Implementation

Numbering of the degrees of freedom (DoFs)

Constructor & Destructor Documentation

§ FE_Q_Bubbles() [1/2]

§ FE_Q_Bubbles() [2/2]

Member Function Documentation

§ get_name()

§ interpolate() [1/3]

§ interpolate() [2/3]

§ interpolate() [3/3]

§ get_interpolation_matrix()

§ get_prolongation_matrix()

§ get_restriction_matrix()

§ has_support_on_face()

§ clone()

§ get_riaf_vector()

§ get_dpo_vector()

Member Data Documentation

§ n_bubbles

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