Abstract: | In this article we consider a spectral Galerkin method with a semi‐implicit Euler scheme for the two‐dimensional Navier‐Stokes equations with H2 or H1 initial data. The H2‐stability analysis of this spectral Galerkin method shows that for the smooth initial data the semi‐implicit Euler scheme admits a large time step. The L2‐error analysis of the spectral Galerkin method shows that for the smoother initial data the numerical solution u exhibits faster convergence on the time interval 0, 1] and retains the same convergence rate on the time interval 1, ∞). © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. |