Non-symmetric (Elliptic)

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).

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 linear elements).

Final mesh (h-FEM with quadratic elements):

Final mesh (h-FEM with quadratic elements).

Final mesh (hp-FEM):

Final mesh (hp-FEM).

DOF convergence graphs:

DOF convergence graph.

CPU time convergence graphs:

CPU convergence graph.

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