Git reference: Benchmark 10-interior-line-singularity.
This example is an extension of Boundary Line Singularity (NIST-07) with an anisotropic solution to allow for a sloped line so that the singularity does not necessarily coincide with element edges.
Equation solved: Poisson equation
(1)-\Delta u - f = 0.
Domain of interest: (-1, 1)^2.
Boundary conditions: Dirichlet, given by exact solution.
u(x,y) = \cos(Ky)\ \ \ \mbox{for}\ x \le 0,\\ u(x,y) = \cos(Ky) + x^{\alpha}\ \ \ \mbox{for}\ x > 0,
where K and \alpha are real constants.
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, isotropic refinements):
Final mesh (hp-FEM, h-anisotropic refinements):
Final mesh (hp-FEM, hp-anisotropic refinements):
DOF convergence graphs:
CPU convergence graphs: