RefHybridFE Class Reference

Class for Hybrid functions, i.e. defined on the boundary of an element. More...

#include <ReferenceFEHybrid.hpp>

Detailed Description

Class for Hybrid functions, i.e. defined on the boundary of an element.

Author

V. Martin

Date

08/2002

This is an enrichment of ReferenceFE in order to implement mixed hybrid finite elements, which are based on a (RT0 - Q0) like discretization of .

This class contains a list of boundary elements; thanks to the Piola transform, the computations are performed on the boundary of the reference element. But in general, the boundary of a 3D reference element is not a 2D reference element.
Example:
REFERENCE TETRA -> 3 REFERENCE TRIA + 1 EQUILATERAL TRIANGLE...
REFERENCE PRISM -> 2 TRIA + 3 QUAD...?
REFERENCE HEXA -> 6 REFERENCE QUAD.

How to add a new finite element ?

• In refFE.h: you add a new finite element flag in FE_TYPE enum with a command like:

  FE_PIPO = a_new_number

• In refHybridFE.h: you declare the functions you need (fct1_Pipo_2D, derfct1_1_Pipo_2D, etc...), the static arrays containing these functions and the coordinates of the nodes on the reference element.

• In defQuadRuleFE.cc: you define these functions (fct1_Pipo_2D, etc...)

• In refFE.h you declare your finite element:

  extern const RefHybridFE fePipo;

• In defQuadRuleFE.cc: you define a list of CurrentFEManifold with a command like:

    #define NB_BDFE_PIPO
  static const CurrentFEManifold BdFE_PIPO_1( feTriaP0, geoLinearTria, quadRuleTria4pt, refcoor_PIPOstd::placeholders::_1, 0 );
  ...

• In defQuadRuleFE.cc: you define a static array containing all the CurrentFEManifold with a command like

  static const CurrentFEManifold HybPIPOList[ NB_BDFE_PIPO ] =
  {
       BdFE_PIPOstd::placeholders::_1, BdFE_PIPOstd::placeholders::_2,
       ...
  };

• In defQuadRuleFE.cc: you define your new element with a command like:

  const ReferenceFEHybrid feTriaPipo("Pipo elements on a tetrahedron", FE_PIPO, TETRA,
                               0, 0, 1, 0, 4, 3, NB_BDFE_PIPO, HybPIPOList, refcoor_PIPO, STANDARD_PATTERN );

  See documentation of ReferenceFEHybrid::ReferenceFEHybrid(...) for a precise description of all arguments.

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

• ReferenceFEHybrid.hpp