Git reference: Benchmark 04-exponential-peak.
This problem has an exponential peak in the interior of the domain.
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) = e^{-\alpha ((x - x_{loc})^{2} + (y - y_{loc})^{2})}
where (x_{loc}, y_{loc}) is the location of the peak, and \alpha determines the strength of the peak.
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: