exact_solution.C File Reference

Go to the source code of this file.

Functions
Real	exact_solution (const Real x, const Real y, const Real t)
	This is the exact solution that we are trying to obtain.

Function Documentation

exact_solution()

Real exact_solution	(	const Real	x,
		const Real	y,
		const Real	t
	)

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 36 of file exact_solution.C.

{
  const Real xo = 0.2;
  const Real yo = 0.2;
  const Real u  = 0.8;
  const Real v  = 0.8;
 
  const Real num =
    pow(x - u*t - xo, 2.) +
    pow(y - v*t - yo, 2.);
 
  const Real den =
    0.01*(4.*t + 1.);
 
  return exp(-num/den)/(4.*t + 1.);
}

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