On the long-time stability of the implicit Euler scheme for the two-dimensional Navier-Stokes equations

Tone, F.; Wirosoetisno, D.

Abstract

In this paper we study the stability for all positive time of the fully implicit Euler scheme for the two-dimensional Navier--Stokes equations. More precisely, we consider the time discretization scheme and with the aid of the discrete Gronwall lemma and the discrete uniform Gronwall lemma we prove that the numerical scheme is stable.

Citation

Tone, F., & Wirosoetisno, D. (2006). On the long-time stability of the implicit Euler scheme for the two-dimensional Navier-Stokes equations. SIAM Journal on Numerical Analysis, 44(1), 29-40. https://doi.org/10.1137/040618527

• Journal Article Type: Article
• Online Publication Date: Jan 1, 2006
• Publication Date: Jan 1, 2006
• Deposit Date: Aug 29, 2008
• Publicly Available Date: Aug 29, 2008
• 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: 44
• Issue: 1
• Pages: 29-40
• DOI: https://doi.org/10.1137/040618527
• Keywords: Navier--Stokes equations, Discrete Gronwall lemmas, Implicit Euler scheme.
• Public URL: https://durham-repository.worktribe.com/output/1599416