NIST-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).

Model problem

Equation solved: Poisson equation

(1)

Domain of interest: Unit Square .

Boundary conditions: Dirichlet, given by exact solution.

Exact solution

where parameter determines the degree of the polynomial solution.

Right-hand side

Obtained by inserting the exact solution into the equation.

Sample solution

Solution for :

Comparison of h-FEM (p=1), h-FEM (p=2) and hp-FEM with anisotropic refinements

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:

hp-FEM with iso, h-aniso and hp-aniso refinements

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: