Git reference: Benchmark 02-reentrant-corner.
This is a reentrant corner problem causing a singularity in the solution.
Equation solved: Laplace equation
(1)-\Delta u = 0.
Domain of interest: (-1, 1)^2 with a section removed from the clockwise side of the positive x axis.
Boundary conditions: Dirichlet, given by exact solution.
u(x, y) = r^{\alpha}\sin(\alpha \theta)
where \alpha = \pi / \omega, r = \sqrt{x^2+y^2}, and \theta = tan^{-1}(y/x). Here \omega determines the angle of the re-entrant corner.
This benchmark has four different versions, we use the global variable PARAM (below) to switch among them.
int PARAM = 1; // PARAM determines which parameter values you wish to use for the strength of the singularity in
// the current (nist-2) Reentrant Corner problem.
// PARAM strength OMEGA ALPHA
// 0: 1 5*Pi/4 4/5
// 1: 2 3*Pi/2 2/3
// 2: 3 7*Pi/4 4/7
// 3: 4 2*Pi 1/2
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, isotropic refinements):
Final mesh (hp-FEM, h-anisotropic refinements):
Final mesh (hp-FEM, hp-anisotropic refinements):
DOF convergence graphs:
CPU convergence graphs: