Git reference: Benchmark 06-boundary-layer.
This example is a singularly perturbed problem that exhibits a boundary layer along the right and top sides of the domain.
Equation solved: Convection-diffusion equation with first order terms.
-\epsilon \nabla^{2} u + 2\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} - f = 0.
Domain of interest: (-1, 1)^2.
Boundary conditions: Dirichlet, given by exact solution.
u(x,y) = (1 - e^{-(1 - x) / \epsilon})(1 - e^{-(1 - y) / \epsilon})cos(\pi (x + y))
where \epsilon determines the strength of the boundary layer.
Obtained by inserting the exact solution into the latter 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: