Git reference: Benchmark 07-boundary-line-singularity.
Many papers on testing adaptive algorithms use a 1D example with a singularity of the form x^{\alpha} at the left endpoint of the domain. This can be extended to 2D by simply making the solution be constant in y.
Equation solved: Poisson equation
(1)-\Delta u - f = 0.
Domain of interest: Unit Square (0, 1)^2
Boundary conditions: Dirichlet, given by exact solution.
u(x,y) = x^{\alpha}
where \alpha \geq 0.5 determines the strength of the singularity.
Obtained by inserting the exact solution into the equation.
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: