This problem combines four difficulties of different strengths into the same problem by combining some of the features of the other test problems (reentrant corner, sharp peak, etc).

Equation solved: Poisson equation

(1)

Domain of interest: L-shaped domain \ .

Boundary conditions: Dirichlet, given by exact solution.

Quite complicated, see the source code.

where , and . Here determines the angle of the re-entrant corner.

is the location of the peak, determines the strength of the peak,

and . Here is the center of the circular wave front. is the distance from the wave front to the center of the circle, and gives the steepness of the wave front.

Last but not least, determines the strength of the boundary layer; the boundary layer was placed at .

Final mesh (h-FEM, p=1, anisotropic refinements):

Final mesh (h-FEM, p=2, anisotropic refinements):

Final mesh (hp-FEM, h-anisotropic refinements):

DOF convergence graphs:

CPU convergence graphs:

Final mesh (hp-FEM, h-anisotropic refinements):

Final mesh (hp-FEM, hp-anisotropic refinements):

DOF convergence graphs:

CPU convergence graphs: