Implementation of the default H(grad)-compatible FEM basis of degree 1 on Quadrilateral cell. More...

`#include <Intrepid_HGRAD_QUAD_C1_FEM.hpp>`

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.

Private Member Functions

void initializeTags ()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Detailed Description

Implementation of the default H(grad)-compatible FEM basis of degree 1 on Quadrilateral cell.

Implements Lagrangian basis of degree 1 on the reference Quadrilateral cell. The basis has cardinality 4 and spans a COMPLETE bi-linear 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)       |
|=========|==============|==============|==============|=============|===========================|
|   MAX   |  maxScDim=0  |  maxScOrd=3  |  maxDfOrd=0  |     -       |                           |
|=========|==============|==============|==============|=============|===========================|
```

Member Function Documentation

template<class Scalar , class ArrayScalar >
 void Intrepid::Basis_HGRAD_QUAD_C1_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar & outputValues, const ArrayScalar & inputPoints, const EOperator operatorType ) const` [inline, 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 >.