Reference Elements
[dune-grid]


Detailed Description

Classes describing the geometry of the reference elements.

Every entity of a grid is obtained by a mapping from the some reference element. The topology of the reference elements needs only to be described once. The reference element describes how an entity is built up hierarchically from entities of lower codimension and what the types of these lower-dimensional entities are.

Here is a graphical representation of the reference elements:

  1. One-dimensional reference element. For d=1 the simplex and cube are identical
    line.png
  2. Two-dimensional reference simplex (a.k.a. triangle)
    triangle.png
  3. Three-dimensional reference simplex (a.k.a. tetrahedron)
    tetrahedron.png

    Face Numbering

    tetrahedron_edges.png

    Edge Numbering

  4. Two-dimensional reference cube (a.k.a. quadrilateral)
    quadrilateral.png
  5. Three-dimensional reference cube (a.k.a. hexahedron)
    hexahedron.png

    Face Numbering

    hexahedron_edges.png

    Edge Numbering

  6. Prism reference element
    prism.png

    Face Numbering

    prism_edges.png

    Edge Numbering

  7. Pyramid reference element
    pyramid.png

    Face Numbering

    pyramid_edges.png

    Edge Numbering

Note that the cube reference elements are available for any dimension.


Classes

class  Dune::ReferenceElement< ctype, dim >
 This is the abstract base class for reference elements. More...
class  Dune::ReferenceElementWrapper< Imp >
 The wrapper allows Imp to be used as a reference element without making methods of Imp virtual. More...
class  Dune::ReferenceCube< ctype, dim >
 This is the reference cube without virtual functions. More...
class  Dune::ReferenceCube< ctype, 0 >
 specialization for d=0 More...
class  Dune::ReferenceCubeContainer< ctype, dim >
 Make the reference cube accessible as a container. More...
class  Dune::ReferenceSimplex< ctype, dim >
 Reference simplex. More...
class  Dune::ReferenceSimplex< ctype, 0 >
 specialization for d=0 More...
class  Dune::ReferenceSimplexContainer< ctype, dim >
 Make the reference simplex accessible as a container. More...
class  Dune::ReferencePrismContainer< ctype, dim >
 Make the reference Prism accessible as a container. More...
class  Dune::ReferencePyramidContainer< ctype, dim >
 Make the reference Pyramid accessible as a container. More...
class  Dune::ReferenceElementContainer< ctype, dim >
 Combines all reference elements. More...
class  Dune::ReferenceElementContainer< ctype, 3 >
 Combines all reference elements for dim==3. More...

Variables

static ReferenceCubeContainer<
ctype, dim > 
Dune::ReferenceElements::cube
 Singleton containing reference hypercubes.
static ReferenceSimplexContainer<
ctype, dim > 
Dune::ReferenceElements::simplices
 Singleton containing reference simplices.
static ReferenceElementContainer<
ctype, dim > 
Dune::ReferenceElements::general
 Singleton containing reference elements.
static ReferenceCubeContainer<
ctype, 3 > 
Dune::ReferenceElements< ctype, 3 >::cube
 Singleton containing reference hexahedra.
static ReferenceSimplexContainer<
ctype, 3 > 
Dune::ReferenceElements< ctype, 3 >::simplices
 Singleton containing reference tetrahedra.
static ReferenceElementContainer<
ctype, 3 > 
Dune::ReferenceElements< ctype, 3 >::general
 Singleton containing 3d reference elements.
static ReferencePrismContainer<
ctype, 3 > 
Dune::ReferenceElements< ctype, 3 >::prism
 Singleton containing reference prisms.
static ReferencePyramidContainer<
ctype, 3 > 
Dune::ReferenceElements< ctype, 3 >::pyramid
 Singleton containing reference pyramids.

Variable Documentation

template<typename ctype>
ReferenceCubeContainer< ctype, 3 > Dune::ReferenceElements< ctype, 3 >::cube [inline, static, inherited]

Singleton containing reference hexahedra.

template<typename ctype, int dim>
ReferenceCubeContainer< ctype, dim > Dune::ReferenceElements< ctype, dim >::cube [inline, static, inherited]

Singleton containing reference hypercubes.

template<typename ctype>
ReferenceElementContainer< ctype, 3 > Dune::ReferenceElements< ctype, 3 >::general [inline, static, inherited]

Singleton containing 3d reference elements.

template<typename ctype, int dim>
ReferenceElementContainer< ctype, dim > Dune::ReferenceElements< ctype, dim >::general [inline, static, inherited]

Singleton containing reference elements.

template<typename ctype>
ReferencePrismContainer< ctype, 3 > Dune::ReferenceElements< ctype, 3 >::prism [inline, static, inherited]

Singleton containing reference prisms.

template<typename ctype>
ReferencePyramidContainer< ctype, 3 > Dune::ReferenceElements< ctype, 3 >::pyramid [inline, static, inherited]

Singleton containing reference pyramids.

template<typename ctype>
ReferenceSimplexContainer< ctype, 3 > Dune::ReferenceElements< ctype, 3 >::simplices [inline, static, inherited]

Singleton containing reference tetrahedra.

template<typename ctype, int dim>
ReferenceSimplexContainer< ctype, dim > Dune::ReferenceElements< ctype, dim >::simplices [inline, static, inherited]

Singleton containing reference simplices.

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