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

被引：61

作者：

Tone, F ^{[1
]}

Wirosoetisno, D ^{[1
]}

机构：

[1] Indiana Univ, Inst Appl Math & Sci Comp, Bloomington, IN 47405 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2006年 / 44卷 / 01期

关键词：

Navier-Stokes equations; discrete Gronwall lemmas; implicit Euler scheme;

D O I：

10.1137/040618527

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：29 / 40

页数：12

共 13 条

[1]

[Anonymous], 1997, APPL MATH SCI

[2]

BERNARDI C, 1992, MATH APPL BERLIN, V10

[3]

FOIAS C, 2001, ENCY MATH APPL, V83

[4]

GEVECI T, 1989, MATH COMPUT, V53, P43, DOI 10.1090/S0025-5718-1989-0969488-5

[5]

Girault V., 1979, LECT NOTES MATH, V749

[6]

Gottlieb D., 1977, CBMS NSF REGIONAL C, V26

[7] FINITE-ELEMENT APPROXIMATION OF THE NONSTATIONARY NAVIER-STOKES PROBLEM .1. REGULARITY OF SOLUTIONS AND 2ND-ORDER ERROR-ESTIMATES FOR SPATIAL DISCRETIZATION [J].

HEYWOOD, JG ;

RANNACHER, R .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (02) :275-311

[8]

Jie Shen, 1990, Applicable Analysis, V38, P201, DOI 10.1080/00036819008839963

[9] On the global stability of a temporal discretization scheme for the Navier-Stokes equations [J].

Ju, N .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2002, 22 (04) :577-597

[10]

Leray J., 1933, J. Math. Pures Appl, V12, P1

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