Title: A New Efficient Spectral Galerkin Method for Singular
       Perturbation Problems

Authors: W. B. Liu and Jie Shen

Status: J. Sci. Comput. Vol. 11, 411-437, 1996

Abstract:

 A new spectral Galerkin method is proposed for the
convection-dominated convection-diffusion equation.  This method
employs a new class of trail function spaces. The available error
bounds provide a clear theoretical interpretation for the higher
accuracy of the new method compared to the conventional spectral
methods when applied to problems with thin boundary layers. Efficient
solution techniques are developed for the convection-diffusion
equations by using appropriate basis functions for the new trial
function spaces.  The higher accuracy and the effectiveness of the new
method for problems with thin boundary layers are confirmed by our
numerical experiments.