Space of scalar valued finite element functions on a Mesh. More...

#include <lf/fe/fe.h>

Inheritance diagram for lf::fe::ScalarFESpace< SCALAR >:

Public Types
using	Scalar = SCALAR

Public Member Functions
virtual std::shared_ptr< const lf::mesh::Mesh >	Mesh () const =0
	acess to underlying mesh

virtual const lf::assemble::DofHandler &	LocGlobMap () const =0
	access to associated local-to-global map

virtual ScalarReferenceFiniteElement< SCALAR > const *	ShapeFunctionLayout (const lf::mesh::Entity &entity) const =0
	access to shape function layout for mesh entities

virtual size_type	NumRefShapeFunctions (const lf::mesh::Entity &entity) const =0
	number of interior shape functions associated to a particular mesh entity.

virtual	~ScalarFESpace ()=default
	No special destructor.

Protected Member Functions
	ScalarFESpace ()=default
	default constructor, needed by std::vector

	ScalarFESpace (const ScalarFESpace &)=default

	ScalarFESpace (ScalarFESpace &&) noexcept=default

ScalarFESpace &	operator= (const ScalarFESpace &)=default

ScalarFESpace &	operator= (ScalarFESpace &&) noexcept=default

Detailed Description

template<typename SCALAR>
class lf::fe::ScalarFESpace< SCALAR >

Space of scalar valued finite element functions on a Mesh.

Template Parameters

SCALAR Scalar type of the finite element functions, usually either double or complex<double>

A ScalarFESpace can be thought of as a set of basis functions \( b^1, \ldots b^N \) which span a (approximation) space \( V_h := \operatorname{span} \{ b^1, \ldots b^N\} \). The basis functions \( b^i\) are usually selected such that their support is limited to a small number of mesh cells. This is reflected in the design of ScalarFESpace:

ShapeFunctionLayout() returns a ScalarReferenceFiniteElement for an entity which describes only the shape functions which are non-zero on this entity (respectively whose support intersects with the entity). In other words, the ScalarReferenceFiniteElement for an entity \( e \) describes the restriction of the approximation space \( \left. V_h \right|_e \) (keep in mind that for technical reasons the shape functions of the ScalarReferenceFiniteElement are defined on a reference element!)
LocGlobMap() returns a DofHandler which identifies the local basis function (returned by ShapeFunctionLayout()) with some of the global basis functions \( b^1\ldots b^N \)

This class is covered in Paragraph 2.8.3.28.

Relation to uscalfe::UniformScalarFESpace

As you can see in the inheritance diagram, every UniformScalarFESpace is also a ScalarFESpace. The UniformScalarFESpace class and all other classes in the namespace lf::uscalfe make additionally the assumption that when we restrict the basis functions \( b^1, \ldots b^N\) to a cell, the remaining set of basis functions are always the same for every cell/reference element (when defined on the reference element). I.e. ShapeFunctionLayout() will always return the same ScalarReferenceFiniteElement for the same reference element.

Definition at line 65 of file scalar_fe_space.h.

Member Typedef Documentation

◆ Scalar

template<typename SCALAR>

using lf::fe::ScalarFESpace< SCALAR >::Scalar = SCALAR

Definition at line 67 of file scalar_fe_space.h.

Constructor & Destructor Documentation

◆ ScalarFESpace() [1/3]

template<typename SCALAR>

lf::fe::ScalarFESpace< SCALAR >::ScalarFESpace ( )

protecteddefault

default constructor, needed by std::vector

Note: creates an invalid object that cannot be used.

Referenced by lf::fe::HierarchicScalarFESpace< SCALAR >::HierarchicScalarFESpace(), operator=(), operator=(), ScalarFESpace(), ScalarFESpace(), lf::uscalfe::UniformScalarFESpace< SCALAR >::UniformScalarFESpace(), and ~ScalarFESpace().

◆ ScalarFESpace() [2/3]

template<typename SCALAR>

lf::fe::ScalarFESpace< SCALAR >::ScalarFESpace ( const ScalarFESpace< SCALAR > & )

protecteddefault

References ScalarFESpace().

◆ ScalarFESpace() [3/3]

template<typename SCALAR>

lf::fe::ScalarFESpace< SCALAR >::ScalarFESpace ( ScalarFESpace< SCALAR > && )

protecteddefaultnoexcept

References ScalarFESpace().

◆ ~ScalarFESpace()

template<typename SCALAR>

virtual lf::fe::ScalarFESpace< SCALAR >::~ScalarFESpace ( )

virtualdefault

No special destructor.

References ScalarFESpace().

Member Function Documentation

◆ LocGlobMap()

template<typename SCALAR>

virtual const lf::assemble::DofHandler & lf::fe::ScalarFESpace< SCALAR >::LocGlobMap ( ) const

nodiscardpure virtual

access to associated local-to-global map

Returns: a reference to the lf::assemble::DofHandler object (immutable)

Implemented in lf::fe::HierarchicScalarFESpace< SCALAR >, and lf::uscalfe::UniformScalarFESpace< SCALAR >.

References LocGlobMap().

Referenced by lf::fe::InitEssentialConditionFromFunction(), and LocGlobMap().

◆ Mesh()

template<typename SCALAR>

virtual std::shared_ptr< const lf::mesh::Mesh > lf::fe::ScalarFESpace< SCALAR >::Mesh ( ) const

nodiscardpure virtual

acess to underlying mesh

Returns: a shared pointer to the mesh

Implemented in lf::fe::HierarchicScalarFESpace< SCALAR >, and lf::uscalfe::UniformScalarFESpace< SCALAR >.

References Mesh().

Referenced by lf::fe::InitEssentialConditionFromFunction(), and Mesh().

◆ NumRefShapeFunctions()

template<typename SCALAR>

virtual size_type lf::fe::ScalarFESpace< SCALAR >::NumRefShapeFunctions ( const lf::mesh::Entity & entity ) const

nodiscardpure virtual

number of interior shape functions associated to a particular mesh entity.

Parameters

entity mesh entity to be queried

Returns: number of interior shape functions

Implemented in lf::fe::HierarchicScalarFESpace< SCALAR >, and lf::uscalfe::UniformScalarFESpace< SCALAR >.

References NumRefShapeFunctions().

Referenced by NumRefShapeFunctions().

◆ operator=() [1/2]

template<typename SCALAR>

ScalarFESpace & lf::fe::ScalarFESpace< SCALAR >::operator= ( const ScalarFESpace< SCALAR > & )

protecteddefault

References ScalarFESpace().

◆ operator=() [2/2]

template<typename SCALAR>

ScalarFESpace & lf::fe::ScalarFESpace< SCALAR >::operator= ( ScalarFESpace< SCALAR > && )

protecteddefaultnoexcept

References ScalarFESpace().

◆ ShapeFunctionLayout()

template<typename SCALAR>

virtual ScalarReferenceFiniteElement< SCALAR > const * lf::fe::ScalarFESpace< SCALAR >::ShapeFunctionLayout ( const lf::mesh::Entity & entity ) const

nodiscardpure virtual

access to shape function layout for mesh entities

Parameters

entity The entity to get the reference element for

Warning: NULL pointers may be returned by this method in case a finite element specification was not given for a particular topological type of entity.