A stabilized finite volume method for Stokes equations using the lowest order P1 − P0 element pair

被引：0
作者：
Tie Zhang
Lixin Tang
机构：
[1] Northeastern University,Department of Mathematics and the State Key Laboratory of SAPI, Research Center of National Metallurgical Automation
[2] Northeastern University,The State Key Laboratory of Synthetical Automation for Process Industries, Research Center of National Metallurgical Automation
来源：
Advances in Computational Mathematics | 2015年 / 41卷
关键词：
Finite volume element; Stokes problem; Stabilized method; − ; element pair; 65N30; 65M60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present a new stabilized finite volume method for Stokes problem using the lowest order P1 − P0 element pair. To offset the lack of the inf -sup condition, a simple jump term of discrete pressure is added to the continuity approximation equation. A discrete inf -sup condition is established for this stabilized scheme. The optimal error estimates are given in the H1- and L2-norms for velocity and in the L2-norm for pressure, respectively.
引用
收藏
页码：781 / 798
页数：17
相关论文
共 64 条
[11]  
Tezduyar T(2000)Error estimates in Math. Comp. 69 103-120
[12]  
Blasco J(1997), Numer. Methods PDEs. 13 147-162
[13]  
Codina R(1997), Math. Comp. 217 85-104
[14]  
Bochev PB(1998) in covolume methods for elliptic and parabolic problem: a unified approach SIAM J. Numer. Anal. 35 494-507
[15]  
Dohrmann CR(2000)Analysis and convergence of a MAC scheme for the generalized Stokes problem Numer. Math. 87 59-81
[16]  
Gunzburger MD(1973)Analysis and convergence of a covolume method for the generalized Stokes problem RAIRO 3 33-76
[17]  
Cai ZQ(2010)A covolume method based on rotated bilinears for the generalized Stokes problem SIAM J. Numer. Anal. 48 824-839
[18]  
Chen ZY(2004)Analysis of a pressure stabilized finite element approximation of the stationary Navier-Stokes equations Int. J. Numer. Methods Fluids 46 183-201
[19]  
Chen ZY(1989)Comforming and noncomforming finite element methods for sovling the stationary Stokes equations Math. Comp. 52 495-508
[20]  
Li RH(2002)Unified analysis of finite volume methods for the Stokes equations SIAM J. Numer. Anal. 39 1865-1888
1234567