A stabilized finite volume method for the stationary Navier-Stokes equations

被引：14

作者：

Sheng, Ying ^{[1
]}

Zhang, Tie ^{[1
]}

Jiang, Zhong-Zhong ^{[2
,3
]}

机构：

[1] Northeastern Univ, Coll Sci, Dept Math, Shenyang 110004, Peoples R China

[2] Northeastern Univ, Sch Business Adm, Dept Informat Management & Decis Sci, Shenyang 110169, Peoples R China

[3] Northeastern Univ, Sch Business Adm, Inst Behav & Serv Operat Management, Shenyang 110169, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2016年 / 89卷

基金：

中国国家自然科学基金;

关键词：

Finite volume method; Navier-Stokes problem; Stabilized method; P-1-P-0 element pair; Inf-sup condition; ELEMENT-METHOD; SUPERCONVERGENCE; APPROXIMATION; FORMULATION; PROJECTION;

D O I：

10.1016/j.chaos.2016.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we propose a stabilized finite volume element method for the Navier-Stokes equations using the lowest order P-1-P-0 element pair. The stabilized method is designed by adding a jump term of the discrete pressure to the continuity approximation equation. A discrete inf-sup condition is established for the stabilized finite volume element scheme which assures the stability of the discrete solutions. The optimal error estimates are derived in the H-1-norm for velocity and the L-2-norm for pressure, respectively. Moreover, the optimal L-2- error estimate is also given for velocity approximation. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：363 / 372

页数：10

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