Space of scalar valued finite element functions on a Mesh. More...
#include <lf/fe/fe.h>
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
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 doubleorcomplex<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
| using lf::fe::ScalarFESpace< SCALAR >::Scalar = SCALAR |
Definition at line 67 of file scalar_fe_space.h.
Constructor & Destructor Documentation
◆ ScalarFESpace() [1/3]
|
protecteddefault |
default constructor, needed by std::vector
- Note
- creates an invalid object that cannot be used.
◆ ScalarFESpace() [2/3]
|
protecteddefault |
◆ ScalarFESpace() [3/3]
|
protecteddefaultnoexcept |
◆ ~ScalarFESpace()
|
virtualdefault |
No special destructor.
Member Function Documentation
◆ LocGlobMap()
|
pure 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 >.
Referenced by lf::fe::InitEssentialConditionFromFunction().
◆ Mesh()
|
pure virtual |
acess to underlying mesh
- Returns
- a shared pointer to the mesh
Implemented in lf::fe::HierarchicScalarFESpace< SCALAR >, and lf::uscalfe::UniformScalarFESpace< SCALAR >.
Referenced by lf::fe::InitEssentialConditionFromFunction().
◆ NumRefShapeFunctions()
|
pure 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 >.
◆ operator=() [1/2]
|
protecteddefault |
◆ operator=() [2/2]
|
protecteddefaultnoexcept |
◆ ShapeFunctionLayout()
|
pure 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.
- Note
- The returned ShapeFunctionLayout pointer will remain for the entire lifetime of the owning ScalarFESpace.
- See also
- ScalarReferenceFiniteElement
Implemented in lf::fe::HierarchicScalarFESpace< SCALAR >, and lf::uscalfe::UniformScalarFESpace< SCALAR >.
Referenced by lf::fe::InitEssentialConditionFromFunction().
The documentation for this class was generated from the following file:
- /__w/lehrfempp/lehrfempp/lib/lf/fe/scalar_fe_space.h
