Abstract

This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global attractors and invariant measures of the scheme to those of the Navier-Stokes equations at vanishing timestep. © 2012 Society for Industrial and Applied Mathematics.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant 0959382

Keywords and Phrases

Collocation; Global Attractor; Invariant Measures; Semi-Implicit Schemes; Spectral; Two-Dimensional Navier-Stokes Equations

International Standard Serial Number (ISSN)

0036-1429

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2023 Society for Industrial and Applied Mathematics, All rights reserved.

Publication Date

28 May 2012

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