The hp finite element method for singularly perturbed problems in nonsmooth domains

We consider the numerical approximation of singularly perturbed elliptic boundary value problems over nonsmooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield finite element spaces with robust approximation properties. In particular, we construct an hp finite element space that approximates all components uniformly, at a near exponential rate. (C) 1999 John Wiley & Sons, Inc.