A new stable second order nonconforming mixed finite element scheme for the stationary Stokes and Navier-Stokes equations

被引：6
|
作者：
Shi, Dongyang [1 ]
Gong, Wei [2 ]
Ren, Jincheng [3 ]
机构：
[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
[3] Shangqiu Normal Univ, Dept Math, Shangqiu 476000, Peoples R China
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2011年 / 53卷 / 9-10期
基金：
中国国家自然科学基金;
关键词：
Stationary Stokes and Navier-Stokes equations; Nonconforming mixed finite element scheme; Inf-sup condition; Optimal error estimates;
D O I：
10.1016/j.mcm.2011.01.026
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, the discretization of the stationary Stokes and Navier-Stokes equations in a two-dimensional domain by a nonconforming mixed finite element method is considered. The standard formulation of the Stokes and Navier-Stokes equations in the primitive variables is formed, which takes for approximating space the new nonconforming rectangular element for the velocity and the bilinear element for the pressure. The optimal error estimates for the approximations of both the velocity in broken H(1)-norm and the pressure in L(2)-norm are achieved. Numerical experiments are given which are consistent with our theoretical analysis. (C) 2011 Elsevier Ltd. All rights reserved.
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页码：1956 / 1969
页数：14
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