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 quadratic elements):

Final mesh (hp-FEM):

DOF convergence graphs:

CPU time convergence graphs:

Non-symmetric (Elliptic)¶

Model problem¶

Exact solution¶

Sample solution¶

Convergence comparison¶

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Non-symmetric (Elliptic)¶

Model problem¶

Exact solution¶

Sample solution¶

Convergence comparison¶

Table Of Contents

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