Git reference: Benchmark 01-analytic-solution.
The purpose of this benchmark is to observe how an adaptive algorithm behaves in a context where adaptivity isn’t really needed (smooth solution).
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) = 2^{4p}x^{p}(1-x)^{p}y^{p}(1-y)^p
where parameter p determines the degree of the polynomial solution.
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: