A posteriori H-1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

摘要

The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H-1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Three modifications of these estimators are introduced and discussed.Much attention is given to the performance of the error estimator in numerical experiments. This helps to identify those estimators that are suitable for practical applications.