Effective spectral approximations of convection-diffusion equations

We propose two approaches for the spectral approximation of convection-diffusion problems with thin layers. The first is based upon stabilization methods of Petrov-Galerkin type that generalize those proposed in recent years in the framework of finite elements. The second is a heterogeneous domain decomposition which is extremely effective whenever layer location can be predicted a priori. A third method stems from a combined approach in which a low order stabilization method is applied as a pre-processor for the heterogeneous domain decomposition method. © 1994 Elsevier Science B.V. All rights reserved.