Stability and convergence analysis of a Crank-Nicolson leap-frog scheme for the unsteady incompressible Navier-Stokes equations

被引：12

作者：

Tang, Qili ^{[1
,2
]}

Huang, Yunqing ^{[1
]}

机构：

[1] Xiangtan Univ, Key Lab Intelligent Comp & Informat Proc, Hunan Key Lab Computat & Simulat Sci & Engn, Minist Educ,Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

[2] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2018年 / 124卷

基金：

中国博士后科学基金;

关键词：

Almost unconditional stability; Finite element method; CNLF; Semi-implicit scheme; Navier-Stokes; FINITE-ELEMENT APPROXIMATION; MAXWELLS EQUATIONS; GALERKIN METHOD; SPATIAL DISCRETIZATION; ERROR ANALYSIS; METAMATERIALS; REGULARITY;

D O I：

10.1016/j.apnum.2017.09.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fully discrete Crank-Nicolson leap-frog (CNLF) scheme is presented and studied for the nonstationary incompressible Navier-Stokes equations. The proposed scheme deals with the spatial discretization by Galerkin finite element method (FEM), treats the temporal discretization by CNLF method for the linear term and the semi-implicit method for nonlinear term. The almost unconditional stability, i.e., the time step is no more than a constant, is proven. By a new negative norm technique, the L-2-optimal error estimates with respect to temporal and spacial orientation for the velocity are derived. At last, some numerical results are provided to justify our theoretical analysis. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：110 / 129

页数：20

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