MFEM  v4.2.0 Finite element discretization library
mfem::FiniteElement Class Referenceabstract

Abstract class for all finite elements. More...

#include <fe.hpp>

Inheritance diagram for mfem::FiniteElement:
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## Public Types

enum  RangeType { SCALAR, VECTOR }
Enumeration for range_type and deriv_range_type. More...

enum  MapType { VALUE, INTEGRAL, H_DIV, H_CURL }
Enumeration for MapType: defines how reference functions are mapped to physical space. More...

enum  DerivType { NONE, GRAD, DIV, CURL }
Enumeration for DerivType: defines which derivative method is implemented. More...

## Public Member Functions

FiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
Construct FiniteElement with given. More...

int GetDim () const
Returns the reference space dimension for the finite element. More...

Geometry::Type GetGeomType () const
Returns the Geometry::Type of the reference element. More...

int GetDof () const
Returns the number of degrees of freedom in the finite element. More...

int GetOrder () const
Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order. More...

bool HasAnisotropicOrders () const
Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions. More...

const int * GetAnisotropicOrders () const
Returns an array containing the anisotropic orders/degrees. More...

int Space () const
Returns the type of FunctionSpace on the element. More...

int GetRangeType () const
Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}. More...

int GetDerivRangeType () const
Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR. More...

int GetMapType () const
Returns the FiniteElement::MapType of the element describing how reference functions are mapped to physical space, one of {VALUE, INTEGRAL H_DIV, H_CURL}. More...

int GetDerivType () const
Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}. More...

int GetDerivMapType () const
Returns the FiniteElement::DerivType of the element describing how reference function derivatives are mapped to physical space, one of {VALUE, INTEGRAL, H_DIV, H_CURL}. More...

virtual void CalcShape (const IntegrationPoint &ip, Vector &shape) const =0
Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip. More...

void CalcPhysShape (ElementTransformation &Trans, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans. More...

virtual void CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const =0
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip. More...

void CalcPhysDShape (ElementTransformation &Trans, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans. More...

const IntegrationRuleGetNodes () const
Get a const reference to the nodes of the element. More...

virtual void CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip. More...

virtual void CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans. More...

void CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
Equivalent to the CalcVShape() method with the same arguments. More...

virtual void CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip. More...

void CalcPhysDivShape (ElementTransformation &Trans, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans. More...

virtual void CalcCurlShape (const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip. More...

void CalcPhysCurlShape (ElementTransformation &Trans, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in physical space at the point described by Trans. More...

virtual void GetFaceDofs (int face, int **dofs, int *ndofs) const
Get the dofs associated with the given face. *dofs is set to an internal array of the local dofc on the face, while *ndofs is set to the number of dofs on that face. More...

virtual void CalcHessian (const IntegrationPoint &ip, DenseMatrix &Hessian) const
Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip. More...

virtual void CalcPhysHessian (ElementTransformation &Trans, DenseMatrix &Hessian) const
Evaluate the Hessian of all shape functions of a scalar finite element in reference space at the given point ip. More...

virtual void CalcPhysLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
Evaluate the Laplacian of all shape functions of a scalar finite element in reference space at the given point ip. More...

virtual void CalcPhysLinLaplacian (ElementTransformation &Trans, Vector &Laplacian) const

virtual void GetLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation. More...

virtual void GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. More...

virtual void GetTransferMatrix (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element. More...

virtual void Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. More...

virtual void Project (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. (VectorFiniteElements) More...

virtual void ProjectFromNodes (Vector &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector of values at the finite element nodes and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. Valid for VectorFiniteElements. More...

virtual void ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local finite dimensional space in terms of the degrees of freedom. For VectorFiniteElements, the rows of the coefficient are projected in the vector space. More...

virtual void ProjectDelta (int vertex, Vector &dofs) const
Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs. More...

virtual void Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the projection depends on it. More...

Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it. More...

virtual void ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it. More...

virtual void ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Compute the discrete divergence matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it. More...

Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode. More...

virtual ~FiniteElement ()
Deconstruct the FiniteElement. More...

## Static Public Member Functions

static bool IsClosedType (int b_type)
Return true if the BasisType of b_type is closed (has Quadrature1D points on the boundary). More...

static bool IsOpenType (int b_type)
Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary). More...

static int VerifyClosed (int b_type)
Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary). More...

static int VerifyOpen (int b_type)
Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary). More...

static int VerifyNodal (int b_type)
Ensure that the BasisType of b_type nodal (satisfies the interpolation property). More...

## Protected Attributes

int dim
Dimension of reference space. More...

Geometry::Type geom_type
Geometry::Type of the reference element. More...

int func_space

int range_type

int map_type

int deriv_type

int deriv_range_type

int deriv_map_type

int dof
Number of degrees of freedom. More...

int order
Order/degree of the shape functions. More...

int orders [Geometry::MaxDim]
Anisotropic orders. More...

IntegrationRule Nodes

DenseMatrix vshape

Container for all DofToQuad objects created by the FiniteElement. More...

## Detailed Description

Abstract class for all finite elements.

Definition at line 235 of file fe.hpp.

## Member Enumeration Documentation

Enumeration for DerivType: defines which derivative method is implemented.

Each FiniteElement class implements up to one type of derivative. The value returned by GetDerivType() indicates which derivative method is implemented.

Enumerator
NONE

No derivatives implemented.

Implements CalcDShape methods.

DIV

Implements CalcDivShape methods.

CURL

Implements CalcCurlShape methods.

Definition at line 290 of file fe.hpp.

Enumeration for MapType: defines how reference functions are mapped to physical space.

A reference function $$\hat u(\hat x)$$ can be mapped to a function $$u(x)$$ on a general physical element in following ways:

• $$x = T(\hat x)$$ is the image of the reference point $$\hat x$$
• $$J = J(\hat x)$$ is the Jacobian matrix of the transformation T
• $$w = w(\hat x) = det(J)$$ is the transformation weight factor for square J
• $$w = w(\hat x) = det(J^t J)^{1/2}$$ is the transformation weight factor in general
Enumerator
VALUE

For scalar fields; preserves point values $$u(x) = \hat u(\hat x)$$

INTEGRAL

For scalar fields; preserves volume integrals $$u(x) = (1/w) \hat u(\hat x)$$

H_DIV

For vector fields; preserves surface integrals of the normal component $$u(x) = (J/w) \hat u(\hat x)$$

H_CURL

For vector fields; preserves line integrals of the tangential component $$u(x) = J^{-t} \hat u(\hat x)$$ (square J), $$u(x) = J(J^t J)^{-1} \hat u(\hat x)$$ (general J)

Definition at line 269 of file fe.hpp.

Enumeration for range_type and deriv_range_type.

Enumerator
SCALAR
VECTOR

Definition at line 257 of file fe.hpp.

## Constructor & Destructor Documentation

 mfem::FiniteElement::FiniteElement ( int D, Geometry::Type G, int Do, int O, int F = FunctionSpace::Pk )

Construct FiniteElement with given.

Parameters
 D Reference space dimension G Geometry type (of type Geometry::Type) Do Number of degrees of freedom in the FiniteElement O Order/degree of the FiniteElement F FunctionSpace type of the FiniteElement

Definition at line 25 of file fe.cpp.

 mfem::FiniteElement::~FiniteElement ( )
virtual

Deconstruct the FiniteElement.

Definition at line 384 of file fe.cpp.

## Member Function Documentation

 void mfem::FiniteElement::CalcCurlShape ( const IntegrationPoint & ip, DenseMatrix & curl_shape ) const
virtual

Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip.

Each row of the result DenseMatrix curl_shape contains the components of the curl of one vector shape function. The size (dof x CDim) of curl_shape must be set in advance, where CDim = 3 for dim = 3 and CDim = 1 for dim = 2.

Definition at line 68 of file fe.cpp.

 void mfem::FiniteElement::CalcDivShape ( const IntegrationPoint & ip, Vector & divshape ) const
virtual

Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip.

The size (dof) of the result Vector divshape must be set in advance.

Definition at line 54 of file fe.cpp.

 virtual void mfem::FiniteElement::CalcDShape ( const IntegrationPoint & ip, DenseMatrix & dshape ) const
pure virtual
 void mfem::FiniteElement::CalcHessian ( const IntegrationPoint & ip, DenseMatrix & Hessian ) const
virtual

Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix Hessian contains upper triangular part of the Hessian of one shape function. The order in 2D is {u_xx, u_xy, u_yy}. The size (dof x (dim (dim+1)/2) of Hessian must be set in advance.

Definition at line 105 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysCurlShape ( ElementTransformation & Trans, DenseMatrix & curl_shape ) const

Evaluate the curl of all shape functions of a vector finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix curl_shape contains the components of the curl of one vector shape function. The size (dof x CDim) of curl_shape must be set in advance, where CDim = 3 for dim = 3 and CDim = 1 for dim = 2.

Definition at line 75 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysDivShape ( ElementTransformation & Trans, Vector & divshape ) const

Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans.

The size (dof) of the result Vector divshape must be set in advance.

Definition at line 61 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysDShape ( ElementTransformation & Trans, DenseMatrix & dshape ) const

Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (dof x SDim) of dshape must be set in advance, where SDim >= dim is the physical space dimension as described by Trans.

Definition at line 201 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysHessian ( ElementTransformation & Trans, DenseMatrix & Hessian ) const
virtual

Evaluate the Hessian of all shape functions of a scalar finite element in reference space at the given point ip.

The size (dof, dim*(dim+1)/2) of Hessian must be set in advance.

Definition at line 299 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysLaplacian ( ElementTransformation & Trans, Vector & Laplacian ) const
virtual

Evaluate the Laplacian of all shape functions of a scalar finite element in reference space at the given point ip.

The size (dof) of Laplacian must be set in advance.

Definition at line 212 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysLinLaplacian ( ElementTransformation & Trans, Vector & Laplacian ) const
virtual

Definition at line 254 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysShape ( ElementTransformation & Trans, Vector & shape ) const

Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans.

The size (dof) of the result Vector shape must be set in advance.

Definition at line 191 of file fe.cpp.

 void mfem::FiniteElement::CalcPhysVShape ( ElementTransformation & Trans, DenseMatrix & shape ) const
inline

Equivalent to the CalcVShape() method with the same arguments.

Definition at line 404 of file fe.hpp.

 virtual void mfem::FiniteElement::CalcShape ( const IntegrationPoint & ip, Vector & shape ) const
pure virtual
 void mfem::FiniteElement::CalcVShape ( const IntegrationPoint & ip, DenseMatrix & shape ) const
virtual

Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip.

Each row of the result DenseMatrix shape contains the components of one vector shape function. The size (dof x dim) of shape must be set in advance.

Definition at line 40 of file fe.cpp.

 void mfem::FiniteElement::CalcVShape ( ElementTransformation & Trans, DenseMatrix & shape ) const
virtual

Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix shape contains the components of one vector shape function. The size (dof x SDim) of shape must be set in advance, where SDim >= dim is the physical space dimension as described by Trans.

Definition at line 47 of file fe.cpp.

 const int* mfem::FiniteElement::GetAnisotropicOrders ( ) const
inline

Returns an array containing the anisotropic orders/degrees.

Definition at line 326 of file fe.hpp.

 int mfem::FiniteElement::GetDerivMapType ( ) const
inline

Returns the FiniteElement::DerivType of the element describing how reference function derivatives are mapped to physical space, one of {VALUE, INTEGRAL, H_DIV, H_CURL}.

Definition at line 352 of file fe.hpp.

 int mfem::FiniteElement::GetDerivRangeType ( ) const
inline

Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR.

Definition at line 336 of file fe.hpp.

 int mfem::FiniteElement::GetDerivType ( ) const
inline

Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}.

Definition at line 347 of file fe.hpp.

 int mfem::FiniteElement::GetDim ( ) const
inline

Returns the reference space dimension for the finite element.

Definition at line 309 of file fe.hpp.

 int mfem::FiniteElement::GetDof ( ) const
inline

Returns the number of degrees of freedom in the finite element.

Definition at line 315 of file fe.hpp.

virtual

Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode.

See the documentation for DofToQuad for more details.

Definition at line 376 of file fe.cpp.

 void mfem::FiniteElement::GetFaceDofs ( int face, int ** dofs, int * ndofs ) const
virtual

Get the dofs associated with the given face. *dofs is set to an internal array of the local dofc on the face, while *ndofs is set to the number of dofs on that face.

Reimplemented in mfem::Linear3DFiniteElement.

Definition at line 100 of file fe.cpp.

 Geometry::Type mfem::FiniteElement::GetGeomType ( ) const
inline

Returns the Geometry::Type of the reference element.

Definition at line 312 of file fe.hpp.

 void mfem::FiniteElement::GetLocalInterpolation ( ElementTransformation & Trans, DenseMatrix & I ) const
virtual

Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation.

Definition at line 111 of file fe.cpp.

 void mfem::FiniteElement::GetLocalRestriction ( ElementTransformation & Trans, DenseMatrix & R ) const
virtual

Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.

The fine element is the image of the base geometry under the given transformation, Trans.

The assumption in this method is that a subset of the coarse dofs can be expressed only in terms of the dofs of the given fine element.

Rows in R corresponding to coarse dofs that cannot be expressed in terms of the fine dofs will be marked as invalid by setting the first entry (column 0) in the row to infinity().

This method assumes that the dimensions of R are set before it is called.

Definition at line 117 of file fe.cpp.

 int mfem::FiniteElement::GetMapType ( ) const
inline

Returns the FiniteElement::MapType of the element describing how reference functions are mapped to physical space, one of {VALUE, INTEGRAL H_DIV, H_CURL}.

Definition at line 341 of file fe.hpp.

 const IntegrationRule& mfem::FiniteElement::GetNodes ( ) const
inline

Get a const reference to the nodes of the element.

Definition at line 382 of file fe.hpp.

 int mfem::FiniteElement::GetOrder ( ) const
inline

Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.

Definition at line 319 of file fe.hpp.

 int mfem::FiniteElement::GetRangeType ( ) const
inline

Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}.

Definition at line 332 of file fe.hpp.

 void mfem::FiniteElement::GetTransferMatrix ( const FiniteElement & fe, ElementTransformation & Trans, DenseMatrix & I ) const
virtual

Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element.

Trans represents the mapping from the reference element of this element into a subset of the reference space of the element fe, thus allowing the "coarse" FiniteElement to be different from the "fine" FiniteElement as when h-refinement is combined with p-refinement or p-derefinement. It is assumed that both finite elements use the same FiniteElement::MapType.

Definition at line 123 of file fe.cpp.

 bool mfem::FiniteElement::HasAnisotropicOrders ( ) const
inline

Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions.

Definition at line 323 of file fe.hpp.

 static bool mfem::FiniteElement::IsClosedType ( int b_type )
inlinestatic

Return true if the BasisType of b_type is closed (has Quadrature1D points on the boundary).

Definition at line 571 of file fe.hpp.

 static bool mfem::FiniteElement::IsOpenType ( int b_type )
inlinestatic

Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

Definition at line 580 of file fe.hpp.

 void mfem::FiniteElement::Project ( Coefficient & coeff, ElementTransformation & Trans, Vector & dofs ) const
virtual

Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom.

Reimplemented in mfem::BiQuadPos2DFiniteElement, mfem::PositiveFiniteElement, and mfem::NodalFiniteElement.

Definition at line 130 of file fe.cpp.

 void mfem::FiniteElement::Project ( VectorCoefficient & vc, ElementTransformation & Trans, Vector & dofs ) const
virtual

Given a vector coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. (VectorFiniteElements)

Definition at line 136 of file fe.cpp.

 void mfem::FiniteElement::Project ( const FiniteElement & fe, ElementTransformation & Trans, DenseMatrix & I ) const
virtual

Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.

Definition at line 160 of file fe.cpp.

 void mfem::FiniteElement::ProjectCurl ( const FiniteElement & fe, ElementTransformation & Trans, DenseMatrix & curl ) const
virtual

Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

Definition at line 175 of file fe.cpp.

 void mfem::FiniteElement::ProjectDelta ( int vertex, Vector & dofs ) const
virtual

Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs.

Definition at line 154 of file fe.cpp.

 void mfem::FiniteElement::ProjectDiv ( const FiniteElement & fe, ElementTransformation & Trans, DenseMatrix & div ) const
virtual

Compute the discrete divergence matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

Reimplemented in mfem::NodalFiniteElement.

Definition at line 183 of file fe.cpp.

 void mfem::FiniteElement::ProjectFromNodes ( Vector & vc, ElementTransformation & Trans, Vector & dofs ) const
virtual

Given a vector of values at the finite element nodes and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. Valid for VectorFiniteElements.

Definition at line 142 of file fe.cpp.

 void mfem::FiniteElement::ProjectGrad ( const FiniteElement & fe, ElementTransformation & Trans, DenseMatrix & grad ) const
virtual

Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

Definition at line 167 of file fe.cpp.

 void mfem::FiniteElement::ProjectMatrixCoefficient ( MatrixCoefficient & mc, ElementTransformation & T, Vector & dofs ) const
virtual

Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local finite dimensional space in terms of the degrees of freedom. For VectorFiniteElements, the rows of the coefficient are projected in the vector space.

Definition at line 148 of file fe.cpp.

 int mfem::FiniteElement::Space ( ) const
inline

Returns the type of FunctionSpace on the element.

Definition at line 329 of file fe.hpp.

 static int mfem::FiniteElement::VerifyClosed ( int b_type )
inlinestatic

Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary).

Definition at line 589 of file fe.hpp.

 static int mfem::FiniteElement::VerifyNodal ( int b_type )
inlinestatic

Ensure that the BasisType of b_type nodal (satisfies the interpolation property).

Definition at line 606 of file fe.hpp.

 static int mfem::FiniteElement::VerifyOpen ( int b_type )
inlinestatic

Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

Definition at line 598 of file fe.hpp.

## Member Data Documentation

 int mfem::FiniteElement::deriv_map_type
protected

Definition at line 240 of file fe.hpp.

 int mfem::FiniteElement::deriv_range_type
protected

Definition at line 240 of file fe.hpp.

 int mfem::FiniteElement::deriv_type
protected

Definition at line 240 of file fe.hpp.

 int mfem::FiniteElement::dim
protected

Dimension of reference space.

Definition at line 238 of file fe.hpp.

 int mfem::FiniteElement::dof
mutableprotected

Number of degrees of freedom.

Definition at line 243 of file fe.hpp.

mutableprotected

Container for all DofToQuad objects created by the FiniteElement.

Definition at line 253 of file fe.hpp.

 int mfem::FiniteElement::func_space
protected

Definition at line 240 of file fe.hpp.

 Geometry::Type mfem::FiniteElement::geom_type
protected

Geometry::Type of the reference element.

Definition at line 239 of file fe.hpp.

 int mfem::FiniteElement::map_type
protected

Definition at line 240 of file fe.hpp.

 IntegrationRule mfem::FiniteElement::Nodes
protected

Definition at line 246 of file fe.hpp.

 int mfem::FiniteElement::order
mutableprotected

Order/degree of the shape functions.

Definition at line 243 of file fe.hpp.

 int mfem::FiniteElement::orders[Geometry::MaxDim]
mutableprotected

Anisotropic orders.

Definition at line 245 of file fe.hpp.

 int mfem::FiniteElement::range_type
protected

Definition at line 240 of file fe.hpp.

 DenseMatrix mfem::FiniteElement::vshape
mutableprotected

Definition at line 248 of file fe.hpp.

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