Uniform Stability of Spectral Nonlinear Galerkin Methods

This article provides a stability analysis for the backward Euler schemes of time discretization applied to the spatially discrete spectral standard and nonlinear Galerkin approximations of the nonstationary Navier-Stokes equations with some appropriate assumption of the data (λ, u0, f). If the backward Euler scheme with the semi-implicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraint Δt ≤ (2/λλ1). Moreover, if the backward Euler scheme with the explicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraints Δt = O(λ) and Δt = O(λ), respectively, where λ ≤ λ, which shows that the restriction on the time step of the spectral nonlinear Galerkin method is less than that of the spectral standard Galerkin method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004

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