Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems

We consider the numerical approximation of a singularly perturbed reaction-diffusion problem over a square. Two different approaches are compared namely: adaptive isotropic mesh refinement and anisotropic mesh refinement. Thus, we compare the h-refinement and the Shishkin mesh approaches numerically with PLTMG software 1]. It is shown how isotropic elements lead to over-refinement and how anisotropic mesh refinement is much more efficient in thin boundary layers.