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:

-\nabla \cdot (a(x,y) \nabla u) = 0,

Parameter a is piecewise constant, a(x,y) = R in the first and third quadrants, and a(x,y) = 1 in the remaining two quadrants.

Domain of interest: (-1, 1)^2.

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.

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

Final mesh.

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

Final mesh.

DOF convergence graphs:

DOF convergence graph.

CPU convergence graphs:

CPU convergence graph.