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

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Abstract

In 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

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