The hp finite element method for singularly perturbed problems in nonsmooth domains
Date
1999ISSN
0749-159XSource
Numerical Methods for Partial Differential EquationsVolume
15Issue
1Pages
63-89Google Scholar check
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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. © 1999 John Wiley & Sons. Inc. Numer Methods Partial Differential Eq 15: 63-89, 1999.