On the long-time stability of the Crank-Nicolson scheme for the 2D Navier-Stokes equations

被引：17

作者：

Tone, Florentina ^{[1
]}

机构：

[1] Univ W Florida, Dept Math & Stat, Pensacola, FL 32514 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 23卷 / 05期

关键词：

discrete Gronwall lemmas; Navier-Stokes equations; Crank-Nicolson scheme;

D O I：

10.1002/num.20219

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the stability for all positive time of the Crank-Nicolson scheme for the two-dimensional Navier-Stokes equations. More precisely, we consider the Crank-Nicolson time discretization together with a general spatial discretization, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the numerical scheme is stable, provided a CFL-type condition is satisfied. (c) 2007 Wiley Periodicals, Inc.

引用

页码：1235 / 1248

页数：14

共 50 条

[1] The approximation of a Crank-Nicolson scheme for the stochastic Navier-Stokes equations
Yang, Xiaoyuan
Wang, Wei
Duan, Yuanyuan
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (01) : 31 - 43
[2] Stability and convergence of the Crank-Nicolson/Adams-Bashforth scheme for the time-dependent Navier-Stokes equations
He, Yinnian
Sun, Weiwei
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (02) : 837 - 869
[3] A NEW LINEARLY EXTRAPOLATED CRANK-NICOLSON TIME-STEPPING SCHEME FOR THE NAVIER-STOKES EQUATIONS
Ingram, Ross
[J]. MATHEMATICS OF COMPUTATION, 2013, 82 (284) : 1953 - 1973
[4] Stability and convergence analysis of a Crank-Nicolson leap-frog scheme for the unsteady incompressible Navier-Stokes equations
Tang, Qili
Huang, Yunqing
[J]. APPLIED NUMERICAL MATHEMATICS, 2018, 124 : 110 - 129
[5] Numerical implementation of the Crank-Nicolson/Adams-Bashforth scheme for the time-dependent Navier-Stokes equations
He, Yinnian
Li, Jian
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2010, 62 (06) : 647 - 659
[6] A two-level correction method in space and time based on Crank-Nicolson scheme for Navier-Stokes equations
Liu, Qingfang
Hou, Yanren
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (11) : 2520 - 2532
[7] On the long-time stability of the implicit Euler scheme for the 2D space-periodic Navier-Stokes equations
Tone, Florentina
[J]. ASYMPTOTIC ANALYSIS, 2007, 51 (3-4) : 231 - 245
[8] The Crank-Nicolson/Adams-Bashforth Scheme for the Time-Dependent Navier-Stokes Equations with Nonsmooth Initial Data
He, Yinnian
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (01) : 155 - 187
[9] Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations
He, Yinnian
Sun, Weiwei
[J]. MATHEMATICS OF COMPUTATION, 2006, 76 (257) : 115 - 136
[10] The Crank-Nicolson finite spectral element method and numerical simulations for 2D non-stationary Navier-Stokes equations
Luo, Zhendong
Jiang, Wenrui
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (05) : 2276 - 2288

← 1 2 3 4 5 →