NIST-11 (Intersecting Interfaces)

The solution to this problem has a discontinuous derivative along the interfaces, and an infinite derivative at the origin that posses a challenge to adaptive algorithms.

Model problem

Equation solved:

Parameter is piecewise constant, in the first and third quadrants, and in the remaining two quadrants.

Domain of interest: .

Boundary conditions: Dirichlet, given by exact solution.

Exact solution

Quite complicated, see the source code.

Sample solution

Comparison of h-FEM (p=1), h-FEM (p=2) and hp-FEM with anisotropic refinements

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: