Intrepid::Basis_HGRAD_TRI_C2_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Triangle cell. More...

#include <Intrepid_HGRAD_TRI_C2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_TRI_C2_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

List of all members.

Public Member Functions

 Basis_HGRAD_TRI_C2_FEM ()
 Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 Evaluation of a FEM basis on a reference Triangle cell.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const
 FVD basis evaluation: invocation of this method throws an exception.

Private Member Functions

void initializeTags ()
 Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Detailed Description

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HGRAD_TRI_C2_FEM< Scalar, ArrayScalar >

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Triangle cell.

Implements Lagrangian basis of degree 2 on the reference Triangle cell. The basis has cardinality 6 and spans a COMPLETE quadratic polynomial space. Basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined and enumerated as follows:

  =================================================================================================
  |         |           degree-of-freedom-tag table                    |                           |
  |   DoF   |----------------------------------------------------------|      DoF definition       |
  | ordinal |  subc dim    | subc ordinal | subc DoF ord |subc num DoF |                           |
  |=========|==============|==============|==============|=============|===========================|
  |    0    |       0      |       0      |       0      |      1      |   L_0(u) = u(0,0)         |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    1    |       0      |       1      |       0      |      1      |   L_1(u) = u(1,0)         |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    2    |       0      |       2      |       0      |      1      |   L_2(u) = u(0,1)         |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    3    |       1      |       0      |       0      |      1      |   L_3(u) = u(1/2,0)       |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    4    |       1      |       1      |       0      |      1      |   L_4(u) = u(1/2,1/2)     |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    5    |       1      |       2      |       0      |      1      |   L_5(u) = u(0,1/2)       |
  |=========|==============|==============|==============|=============|===========================|
  |   MAX   |  maxScDim=1  |  maxScOrd=2  |  maxDfOrd=0  |     -       |                           |
  |=========|==============|==============|==============|=============|===========================|
  

Definition at line 73 of file Intrepid_HGRAD_TRI_C2_FEM.hpp.


Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_TRI_C2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const [inline, virtual]

Evaluation of a FEM basis on a reference Triangle cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference Triangle cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods .

Parameters:
outputValues [out] - variable rank array with the basis values
inputPoints [in] - rank-2 array (P,D) with the evaluation points
operatorType [in] - the operator acting on the basis functions

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 82 of file Intrepid_HGRAD_TRI_C2_FEMDef.hpp.

References Intrepid::Basis< Scalar, ArrayScalar >::basisCardinality_, Intrepid::Basis< Scalar, ArrayScalar >::basisCellTopology_, Intrepid::Basis< Scalar, ArrayScalar >::getBaseCellTopology(), and Intrepid::Basis< Scalar, ArrayScalar >::getCardinality().


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

Generated on Tue Oct 20 15:10:09 2009 for Intrepid by  doxygen 1.6.1