Stability and error analysis for spectral Galerkin method for the Navier–Stokes equations with L2 initial data

Abstract

AbstractIn this article we consider the spectral Galerkin method with the implicit/explicit Euler scheme for the two‐dimensional Navier–Stokes equations with the L2 initial data. Due to the poor smoothness of the solution on [0,1), we use the the spectral Galerkin method based on high‐dimensional spectral space HM and small time step Δt2 on this interval. While on [1,∞), we use the spectral Galerkin method based on low‐dimensional spectral space Hm(m = O(M1/2)) and large time step Δt. For the spectral Galerkin method, we provide the standard H2‐stability and the L2‐error analysis. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007