deal.II/include/fe/mapping.h File Reference

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Classes

class  Mapping< dim, spacedim >
class  Mapping< dim, spacedim >::InternalDataBase
class  Mapping< dim, spacedim >::ExcInvalidData

Enumerations

enum  MappingType {
  mapping_none = 0x0000, mapping_covariant = 0x0001, mapping_contravariant = 0x0002, mapping_covariant_gradient = 0x0003,
  mapping_contravariant_gradient = 0x0004, mapping_piola = 0x0100, mapping_nedelec = 0x0200, mapping_raviart_thomas = mapping_piola,
  mapping_bdm = mapping_piola
}

Enumeration Type Documentation

The transformation type used for the Mapping::transform() functions.

Special finite elements may need special Mapping from the reference cell to the actual mesh cell. In order to be most flexible, this enum provides an extensible interface for arbitrary transformations. Nevertheless, these must be implemented in the transform() functions of inheriting classes in order to work.

Mappings are usually defined for vectors. If such a MappingType is applied to a rank 2 tensor, it is implied that the mapping is applied to each column.

Enumerator:
mapping_none  No mapping.
mapping_covariant  Covariant mapping.
mapping_contravariant  Contravariant mapping.
mapping_covariant_gradient  Mapping of the gradient of a covariant vector field.
mapping_contravariant_gradient  Mapping of the gradient of a contravariant vector field.
mapping_piola  The Piola transform usually used for Hdiv elements.

Piola transform is the standard transformation of vector valued elements in Hdiv. It amounts to a contravariant transformation scaled by the inverse of the volume element.

If applied to a rank 2 tensor, the mapping class will apply the correct transformation for the gradient of such a vector field.

mapping_nedelec  The mapping used for Nedelec elements.

curl-conforming elements are mapped as covariant vectors. Nevertheless, we introduce a separate mapping type, such that we can use the same flag for the vector and its gradient (the transformation of the gradient differs from the one used by mapping_covariant).

mapping_raviart_thomas  The mapping used for Raviart-Thomas elements.
mapping_bdm  The mapping used for BDM elements.


deal.II documentation generated on Sat Aug 15 16:50:25 2009 by doxygen 1.5.9