FiniteElementData< dim > Class Template Reference
[Base classes]

Inheritance diagram for FiniteElementData< dim >:

Inheritance graph
[legend]

List of all members.

Public Types

enum  Conformity {
  unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04,
  H1 = Hcurl | Hdiv, H2 = 0x0e
}

Public Member Functions

 FiniteElementData ()
 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const unsigned int n_blocks=numbers::invalid_unsigned_int)
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
unsigned int tensor_degree () const
bool conforms (const Conformity) const
unsigned int face_to_cell_index (const unsigned int face_index, const unsigned int face, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false) const
unsigned int face_to_equivalent_cell_index (const unsigned int index) const
bool operator== (const FiniteElementData &) const

Public Attributes

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 blocks
const unsigned int degree
const Conformity conforming_space

Static Public Attributes

static const unsigned int dimension = dim


Detailed Description

template<int dim>
class FiniteElementData< dim >

Dimension independent data for finite elements. See the derived class FiniteElement class for information on its use. All its data are available to the implementation in a concrete finite element class.

Author:
Wolfgang Bangerth, Guido Kanschat, 1998, 1999, 2000, 2001, 2003, 2005

Member Enumeration Documentation

template<int dim>
enum FiniteElementData::Conformity

Enumerator for the different types of continuity a finite element may have. Continuity is measured by the Sobolev space containing the constructed finite element space and is also called this way.

Note that certain continuities may imply others. For instance, a function in H1 is in Hcurl and Hdiv as well.

If you are interested in continuity in the classical sense, then the following relations hold:

  1. H1 implies that the function is continuous over cell boundaries.

  2. H2 implies that the function is continuously differentiable over cell boundaries.

  3. L2 indicates that the element is discontinuous. Since discontinuous elements have no topological couplings between grid cells and code may actually depend on this property, L2 conformity is handled in a special way in the sense that it is not implied by any higher conformity.

In order to test if a finite element conforms to a certain space, use FiniteElementData<dim>::conforms().

Enumerator:
unknown  Indicates incompatible continuities of a system.
L2  Discontinuous elements. See above!
Hcurl  Conformity with the space Hcurl (continuous tangential component of a vector field)
Hdiv  Conformity with the space Hdiv (continuous normal component of a vector field)
H1  Conformity with the space H1 (continuous)
H2  Conformity with the space H2 (continuously differentiable)


Constructor & Destructor Documentation

template<int dim>
FiniteElementData< dim >::FiniteElementData (  ) 

Default constructor. Constructs an element with no dofs. Checking n_dofs_per_cell() is therefore a good way to check if something went wrong.

template<int dim>
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 unsigned int  n_blocks = numbers::invalid_unsigned_int 
)

Constructor, computing all necessary values from the distribution of dofs to geometrcal objects.

Parameters:
dofs_per_object Number of dofs on geometrical objects for each dimension. In this vector, entry 0 refers to dofs on vertices, entry 1 on lines and so on. Its length must be dim+1.
n_components Number of vector components of the element.
degree Maximal polynomial degree in a single direction.
conformity The finite element space has continuity of this Sobolev space.
n_blocks Number of vector blocks.


Member Function Documentation

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_vertex (  )  const

Number of dofs per vertex.

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_line (  )  const

Number of dofs per line. Not including dofs on lower dimensional objects.

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_quad (  )  const

Number of dofs per quad. Not including dofs on lower dimensional objects.

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_hex (  )  const

Number of dofs per hex. Not including dofs on lower dimensional objects.

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_face (  )  const

Number of dofs per face, accumulating degrees of freedom of all lower dimensional objects.

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_cell (  )  const

Number of dofs per cell, accumulating degrees of freedom of all lower dimensional objects.

template<int dim>
template<int structdim>
unsigned int FiniteElementData< dim >::n_dofs_per_object (  )  const [inline]

Return the number of degrees per structdim-dimensional object. For structdim==0, the function therefore returns dofs_per_vertex, for structdim==1 dofs_per_line, etc. This function is mostly used to allow some template trickery for functions that should work on all sorts of objects without wanting to use the different names (vertex, line, ...) associated with these objects.

template<int dim>
unsigned int FiniteElementData< dim >::n_components (  )  const

Number of components.

Referenced by DoFTools::n_components().

template<int dim>
unsigned int FiniteElementData< dim >::n_blocks (  )  const

Number of blocks.

template<int dim>
unsigned int FiniteElementData< dim >::tensor_degree (  )  const

Maximal polynomial degree of a shape function in a single coordinate direction.

This function can be used to determine the optimal quadrature rule.

template<int dim>
bool FiniteElementData< dim >::conforms ( const   Conformity  )  const

Test whether a finite element space conforms to a certain Sobolev space.

Note:
This function will return a true value even if the finite element space has higher regularity than asked for.

template<int dim>
unsigned int FiniteElementData< dim >::face_to_cell_index ( const unsigned int  face_index,
const unsigned int  face,
const bool  face_orientation = true,
const bool  face_flip = false,
const bool  face_rotation = false 
) const

Given an index in the natural ordering of indices on a face, return the index of the same degree of freedom on the cell.

template<int dim>
unsigned int FiniteElementData< dim >::face_to_equivalent_cell_index ( const unsigned int  index  )  const

Deprecated:
This function is just a special version of face_to_cell_index for the face zero. It is therefore of limited use in aplications and most of the time, the other function is what is required.
Given an index in the natural ordering of indices on a face, return the index of an equivalent degree of freedom on the cell.

To explain the concept, consider the case where we would like to know whether a degree of freedom on a face is primitive. Unfortunately, the is_primitive() function in the FiniteElement class takes a cell index, so we would need to find the cell index of the shape function that corresponds to the present face index. This function does that.

Code implementing this would then look like this:

 for (i=0; i<dofs_per_face; ++i)
  if (fe.is_primitive(fe.face_to_equivalent_cell_index(i)))
   ... do whatever

template<int dim>
bool FiniteElementData< dim >::operator== ( const FiniteElementData< dim > &   )  const

Comparison operator.


Member Data Documentation

template<int dim>
const unsigned int FiniteElementData< dim >::dimension = dim [static]

The dimension of the finite element, which is the template parameter dim

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_vertex

Number of degrees of freedom on a vertex.

Referenced by DoFTools::max_dofs_per_vertex().

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_line

Number of degrees of freedom in a line; not including the degrees of freedom on the vertices of the line.

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_quad

Number of degrees of freedom in a quadrilateral; not including the degrees of freedom on the lines and vertices of the quadrilateral.

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_hex

Number of degrees of freedom in a hexahedron; not including the degrees of freedom on the quadrilaterals, lines and vertices of the hecahedron.

template<int dim>
const unsigned int FiniteElementData< dim >::first_line_index

First index of dof on a line.

template<int dim>
const unsigned int FiniteElementData< dim >::first_quad_index

First index of dof on a quad.

template<int dim>
const unsigned int FiniteElementData< dim >::first_hex_index

First index of dof on a hexahedron.

template<int dim>
const unsigned int FiniteElementData< dim >::first_face_line_index

First index of dof on a line for face data.

template<int dim>
const unsigned int FiniteElementData< dim >::first_face_quad_index

First index of dof on a quad for face data.

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_face

Number of degrees of freedom on a face. This is the accumulated number of degrees of freedom on all the objects of dimension up to dim-1 constituting a face.

Referenced by DoFTools::max_dofs_per_face().

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_cell

Total number of degrees of freedom on a cell. This is the accumulated number of degrees of freedom on all the objects of dimension up to dim constituting a cell.

Referenced by DoFTools::max_dofs_per_cell().

template<int dim>
const unsigned int FiniteElementData< dim >::components

Number of vector components of this finite element, and dimension of the image space. For vector-valued finite elements (i.e. when this number is greater than one), the number of vector components is in many cases equal to the number of base elements glued together with the help of the FESystem class. However, for elements like the Nedelec element, the number is greater than one even though we only have one base element.

template<int dim>
const unsigned int FiniteElementData< dim >::blocks

The number of vector blocks a BlockVector for this element should contain. For primitive elements, this is equal to components, but for vector valued base elements it may differ. Actually, in systems this is the sum of the base element multiplicities.

template<int dim>
const unsigned int FiniteElementData< dim >::degree

Maximal polynomial degree of a shape function in a single coordinate direction.

Reimplemented in FE_DGPNonparametric< dim, spacedim >, and FE_Nedelec< dim, spacedim >.

template<int dim>
const Conformity FiniteElementData< dim >::conforming_space

Indicate the space this element conforms to.


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

deal.II documentation generated on Sat Aug 15 16:51:59 2009 by doxygen 1.5.9