Anisotropic mesh refinement for problems with internal and boundary layers

The character of convection-dominated, singularly perturbed boundary value problems requires their special numerical treatment in order to guarantee stability and resolve existing layers with acceptable accuracy. In addition to discretization methods particularly developed for this aim, recently more and more attention has been directed towards adapted triangulations of the computational domain. In this paper, an adaptive strategy based on an anisotropic re nement is developed for nite element methods. Starting from some a priori information about the location of layers, the so-called hybrid meshes are constructed. By these meshes, the exibility of unstructured meshes, good approximation properties in layers, and relatively simple rules for a posteriori anisotropic re nement are combined with each other. The e ciency of this procedure is demonstrated by selected numerical examples