Uniform convergence of discontinuous finite element methods for singularly perturbed reaction-diffusion problems
Two families of discontinuous finite element methods for singularly perturbed reaction-diffusion problems are studied. They contain multiple scales spanning the whole problem domain because of a small perturbation parameters. To solve such a multiscale problem, an anisotropic mesh is proposed. This mesh use a finer mesh inside small scale regions, where boundary layers are located, and elsewhere large scale regions are applied. Uniform optimal error estimates in the energy norm are determined for both families on the anisotropical mesh.
scientific article; zbMATH DE number 1781565
scientific article