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Long time stability of a classical efficient scheme for two-dimensional Navier-Stokes equations

Gottlieb, S; Tone, F; Wang, C; Wang, X; Wirosoetisno, D

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Authors

S Gottlieb

F Tone

C Wang

X Wang



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 semidiscrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudospectral (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 L2 and H1 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.

Citation

Gottlieb, S., Tone, F., Wang, C., Wang, X., & Wirosoetisno, D. (2012). Long time stability of a classical efficient scheme for two-dimensional Navier-Stokes equations. SIAM Journal on Numerical Analysis, 50(1), 126-150. https://doi.org/10.1137/110834901

Journal Article Type Article
Publication Date Jan 1, 2012
Deposit Date Feb 12, 2012
Publicly Available Date Mar 23, 2012
Journal SIAM Journal on Numerical Analysis
Print ISSN 0036-1429
Electronic ISSN 1095-7170
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 50
Issue 1
Pages 126-150
DOI https://doi.org/10.1137/110834901
Keywords Two-dimensional Navier–Stokes equations, Semi-implicit schemes, Global attractor,
Invariant measures, Spectral, Collocation.

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