ShapesP12D Class Reference

Shape functions for P12D elements: Linear functions on Triangles
It contains two types of traces
1) ShapesP12D::Faces are linear functions on Segments, and their degrees of freedom are those associated to the nodes of the Segment. More...

#include <ShapesEvaluated.h>

Inheritance diagram for ShapesP12D:

List of all members.

Public Types
typedef ShapesEvaluated__ < P12D, Triangle_1::Bulk >	Bulk
	Bulk shape functions.
typedef ShapesEvaluated__ < P11D, Line_1::Bulk >	Faces
	Shape functions for FaceOne, FaceTwo and FaceThree.
typedef ShapesEvaluated__ < P12D, Triangle_1::FaceOne >	FaceOne
	Full shape functions for FaceOne.
typedef ShapesEvaluated__ < P12D, Triangle_1::FaceTwo >	FaceTwo
	Full shape functions for FaceTwo.
typedef ShapesEvaluated__ < P12D, Triangle_1::FaceThree >	FaceThree
	Full shape functions for FaceThree.
Static Public Attributes
static const Shape *const	P12D = new Linear<2>
	Shape functions on reference triangle.
static const Shape *const	P11D = new Linear<1>
	Shape functions on reference segment.

Detailed Description

Shape functions for P12D elements: Linear functions on Triangles
It contains two types of traces
1) ShapesP12D::Faces are linear functions on Segments, and their degrees of freedom are those associated to the nodes of the Segment.

2) ShapesP12D::FaceOne, ShapesP12D::FaceTwo, ShapesP12D::FaceThree are the full set of linear shape functions in the element evaluated at quadrature points in each one of the faces. Instead of having then 2 degrees of freedom per field per face, there are here 3 degrees of freedom per field per face. Of course, some of these values are trivially zero, i.e., those of the shape functions associated to the node opposite to the face where the quadrature point is. These are provided since ocassionally it may be necessary to have the boundary fields have the same number of degrees of freedom as the bulk fields. In the most general case of arbitrary bases, there is generally no shape functions that is identically zero on the face, and hence bulk and trace fields have the same number of degrees of freedom. With these shape functions, for example, it is possible to compute the normal derivative of each basis function at the boundary.