This example has a smooth solution that exhibits a steep interior layer.

(2)

where is a parameter (slope of the layer). With larger , this problem becomes difficult for adaptive algorithms, and at the same time the advantage of adaptive -FEM over adaptive low-order FEM becomes more significant. We will use in the following.

Nonconstant Dirichlet, matching the exact solution.

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: