Intrepid

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

List of all members.

## Public Member Functions

Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
FEM basis evaluation on a reference Quadrilateral 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.
void getDofCoords (ArrayScalar &DofCoords) const
Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral.

## Private Member Functions

void initializeTags ()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

## Detailed Description

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

Implements Lagrangian basis of degree 2 on the reference Quadrilateral cell. The basis has cardinality 9 and spans a COMPLETE bi-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(-1,-1)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1,-1)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 1, 1)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    3    |       0      |       3      |       0      |      1      |   L_3(u) = u(-1, 1)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    4    |       1      |       0      |       0      |      1      |   L_4(u) = u( 0,-1)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    5    |       1      |       1      |       0      |      1      |   L_5(u) = u( 1, 0)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    6    |       1      |       2      |       0      |      1      |   L_6(u) = u( 0, 1)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    7    |       1      |       3      |       0      |      1      |   L_7(u) = u(-1, 0)       |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    8    |       2      |       0      |       0      |      1      |   L_8(u) = u( 0, 0)       |
|=========|==============|==============|==============|=============|===========================|
|   MAX   |  maxScDim=2  |  maxScOrd=3  |  maxDfOrd=0  |     -       |                           |
|=========|==============|==============|==============|=============|===========================|

## Member Function Documentation

template<class Scalar , class ArrayScalar >
 void Intrepid::Basis_HGRAD_QUAD_C2_FEM< Scalar, ArrayScalar >::getDofCoords ( ArrayScalar & DofCoords ) const [virtual]

Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral.

Parameters:
 DofCoords [out] - array with the coordinates of degrees of freedom, dimensioned (F,D)

Implements Intrepid::DofCoordsInterface< ArrayScalar >.

template<class Scalar , class ArrayScalar >
 void Intrepid::Basis_HGRAD_QUAD_C2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar & outputValues, const ArrayScalar & inputPoints, const EOperator operatorType ) const [virtual]

FEM basis evaluation on a reference Quadrilateral cell.

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

Parameters:
 outputValues [out] - rank-2 or 3 array with the computed basis values inputPoints [in] - rank-2 array with dimensions (P,D) containing reference points operatorType [in] - operator applied to basis functions

Implements Intrepid::Basis< Scalar, ArrayScalar >.