exact_solution.C File Reference

Go to the source code of this file.

Functions
Real	exact_solution (const int component, const Real x, const Real y, const Real z=0.)
	This is the exact solution that we are trying to obtain.

Function Documentation

exact_solution()

Real exact_solution	(	const int	component,
		const Real	x,
		const Real	y,
		const Real	z = 0.
	)

This is the exact solution that we are trying to obtain.

We will solve

• (u_xx + u_yy) = f

and take a finite difference approximation using this function to get f. This is the well-known "method of manufactured solutions".

Definition at line 39 of file exact_solution.C.

{
  static const Real pi = acos(-1.);
 
  switch (component)
    {
    case 0:
      return cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
    case 1:
      return sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
    case 2:
      return sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z)*cos(.5*pi*x*y*z);
    default:
      libmesh_error_msg("Invalid component = " << component);
    }
 
  // dummy
  return 0.0;
}

References libMesh::pi, and libMesh::Real.