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 stabiliz ation methods of Petrov-Galerkin type that generalize those proposed i n recent years in the framework of finite elements. The second is a he terogeneous 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 applie d as a pre-processor for the heterogeneous domain decomposition method .