Non-symmetric (Elliptic)

Git reference: Benchmark nonsym-check.

This example uses a nonsymmetric equation and its purpose is to check that nonsymmetric problems are solved correctly.

Model problem

Equation solved:

(1)-\Delta u + \frac{\partial u}{\partial x} = f.

Domain of interest: Square domain (0, \pi) x (0, \pi).

Right-hand side:

(2)f(x, y) = sin(x) + cos(x).

Exact solution

(3)u(x,y) = sin(x).

In the code:

// Exact solution.
static double fn(double x, double y)
{
  return sin(x);
}
static double fndd(double x, double y, double& dx, double& dy)
{
  dx = cos(x);
  dy = 0;
  return fn(x, y);
}

Boundary conditions: Zero Dirichlet on left edge, zero Neumann on top and bottom edges, nonzero Neumann on the right edge (all matching exact solution).

Sample solution

Convergence comparison

Final mesh (h-FEM with linear elements):

Final mesh (h-FEM with quadratic elements):

Final mesh (hp-FEM):

DOF convergence graphs:

CPU time convergence graphs: