A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations

被引：88
|
作者：
Cai, ZQ
Douglas, J
Ye, X
机构：
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[2] Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA
来源：
CALCOLO | 1999年 / 36卷 / 04期
关键词：
Finite Element Method; Error Estimate; Stokes Equation; Elliptic Equation; Optimal Error;
D O I：
10.1007/s100920050031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Douglas ct al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component of the velocity in the stationary Stokes and Navier-Stokes equations, along with a piecewise-constant element for the pressure. We obtain a stable element in both cases for which optimal error estimates for the approximation of both the velocity and pressure in L-2 can be established, as well as one in a broken H-1-norm for the velocity.
引用
收藏
页码：215 / 232
页数：18
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