Anisotropic mesh refinement for problems with internal and boundary layers

International Journal for Numerical Methods in Engineering, John Wiley, Vol 46, Num 11, pp.1933-1953, December 1999

MESHING
RESEARCH
CORNER

Correspondence to: T. Skalicky, Institute for Numerical Mathematics, Dresden University of Technology, D 01062 Dresden, Germany.
E-mail: skalicky@math.tu-dresden.de

Abstract
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 refinement is developed for finite element methods. Starting from some a priori information about the location of layers, the so-called hybrid meshes are constructed. By these meshes, the flexibility of unstructured meshes, good approximation properties in layers, and relatively simple rules for a posteriori anisotropic refinement are combined with each other. The efficiency of this procedure is demonstrated by selected numerical examples.