A cheapest nonconforming rectangular finite element for the stationary Stokes problem

被引：8

作者：

Nam, Hyun ^{[1
]}

Choi, Hyung Jun ^{[1
]}

Park, Chunjae ^{[2
]}

Sheen, Dongwoo ^{[1
,3
]}

机构：

[1] Seoul Natl Univ, Dept Math, Seoul 151747, South Korea

[2] Konkuk Univ, Dept Math, Seoul 143701, South Korea

[3] Seoul Natl Univ, Interdisciplinary Program Computat Sci & Technol, Seoul 151747, South Korea

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2013年 / 257卷

关键词：

Stokes equations; Nonconforming finite element; Bubble function; UNIFYING THEORY; STABILIZATION;

D O I：

10.1016/j.cma.2013.01.005

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We introduce a least degrees of freedom nonconforming finite element pair to approximate the Stokes equations based on quadrilateral meshes. The finite element space for the velocity field is composed of the P-1-nonconforming quadrilateral element plus only one additional global DSSY (Douglas-Santos-Sheen-Ye) or RT (Rannacher-Turek) type of bubble function. The pressure field is approximated by the piecewise constant function. We show that the discrete problem is nonsingular and the element pair satisfies a weak discrete inf-sup condition. Several numerical examples are shown to confirm the efficiency and reliability of the proposed method. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：77 / 86

页数：10

共 42 条

[1] P1-NONCONFORMING FINITE ELEMENTS ON TRIANGULATIONS INTO TRIANGLES AND QUADRILATERALS [J].