Stability and convergence of optimum spectral non-linear Galerkin methods

Our objective in this article is to present some numerical schemes for the approximation of the 2-D Navier-Stokes equations with periodic boundary con ditions, and to study the stability and convergence of the schemes. Spatial discretization can be performed by either the spectral Galerkin method or the optimum spectral non-linear Galerkin method; time discretization is don e by the Euler scheme and a two-step scheme. Our results show that under th e same convergence rate the optimum spectral non-linear Galerkin method is superior to the usual Galerkin methods. Finally, numerical example is provi ded and supports our results. Copyright (C) 2001 John Wiley & Sons, Ltd.