Git reference: Benchmark 11-kellogg.
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.
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.
Quite complicated, see the source code.
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: