# Galeri::FiniteElements::AbstractVariational Class Reference

Pure virtual class that defines the variational form. More...

`#include <Galeri_AbstractVariational.h>`

Inheritance diagram for Galeri::FiniteElements::AbstractVariational:
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List of all members.

## Public Member Functions

virtual ~AbstractVariational ()
Destructor.

virtual double LHS (const double Phi, const double Psi, const double PhiX, const double PsiX, const double PhiY, const double PsiY, const double PhiZ, const double PsiZ, const double x, const double y, const double z) const =0
Evaluates the bilinear form (without integral) at point (x,y,z).
virtual double RHS (const double Psi, const double PsiX, const double PsiY, const double PsiZ, const double x, const double y, const double z) const =0
Returns the value of the right-hand side (without integral) at point (x, y, z).

virtual int BC (const int PatchID) const =0
Returns an integer identifying the boundary condition assigned to the specified patch.
virtual double BC (const double x, const double y, const double z, const int PatchID) const =0
Returns the value of the boundary condition at point (x, y, z).

virtual int IntegrateOverElement (const AbstractVariational &Variational, const double *x, const double *y, const double *z, const double *data, double *ElementMatrix, double *ElementRHS) const =0
Integrates the bilinear form and the right-hand side over the element.
virtual int ElementNorm (const double *LocalSol, const double *x, const double *y, const double *z, double *Norm) const =0
Computes the norm of the computed solution over the element.
virtual int ElementNorm (int(*ExactSolution)(double, double, double, double *), const double *x, const double *y, const double *z, double *Norm) const =0
Computed the norm of the exact solution over the element.
virtual int ElementNorm (const double *LocalSol, int(*ExactSolution)(double, double, double, double *), const double *x, const double *y, const double *z, double *Norm) const =0
Computed the norm of the computed and exact solution over the element.

virtual ~AbstractVariational ()
Destructor.

virtual double LHS (const double Phi, const double Psi, const double PhiX, const double PsiX, const double PhiY, const double PsiY, const double PhiZ, const double PsiZ, const double x, const double y, const double z) const =0
Evaluates the bilinear form (without integral) at point (x,y,z).
virtual double RHS (const double Psi, const double PsiX, const double PsiY, const double PsiZ, const double x, const double y, const double z) const =0
Returns the value of the right-hand side (without integral) at point (x, y, z).

virtual int BC (const int PatchID) const =0
Returns an integer identifying the boundary condition assigned to the specified patch.
virtual double BC (const double x, const double y, const double z, const int PatchID) const =0
Returns the value of the boundary condition at point (x, y, z).

virtual int IntegrateOverElement (const AbstractVariational &Variational, const double *x, const double *y, const double *z, const double *data, double *ElementMatrix, double *ElementRHS) const =0
Integrates the bilinear form and the right-hand side over the element.
virtual int ElementNorm (const double *LocalSol, const double *x, const double *y, const double *z, double *Norm) const =0
Computes the norm of the computed solution over the element.
virtual int ElementNorm (int(*ExactSolution)(double, double, double, double *), const double *x, const double *y, const double *z, double *Norm) const =0
Computed the norm of the exact solution over the element.
virtual int ElementNorm (const double *LocalSol, int(*ExactSolution)(double, double, double, double *), const double *x, const double *y, const double *z, double *Norm) const =0
Computed the norm of the computed and exact solution over the element.

## Detailed Description

Pure virtual class that defines the variational form.

AbstractVariational is a pure virtual class, that specifies a set of abstract interfaces, required to integrate the variational form and the right-hand side over an element, and to compute the norm of compute solution, exact solution, and error over the element. A concrete implementation of this class also defined how boundary conditions are resolved.

The element on which the integration is performed is specified by providing the coordinates of the local vertices.

Date:
Last updated on Apr-05.

The documentation for this class was generated from the following files:
• FiniteElements/Galeri_AbstractVariational.h
• fem/Galeri_AbstractVariational.h
Generated on Wed Apr 13 10:08:44 2011 for Galeri by  1.6.3