Anisotropic mesh refinement in stabilized Galerkin methods

The numerical solution of a convection-diffusion-reaction model problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least-squares type accomodates diffusion-dominated as well as convection- and/or reaction-dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.