A STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS

被引：4

作者：

Tian, Wanfu ^{[1
]}

Song, Liqiu ^{[2
]}

Li, Yonghai ^{[3
]}

机构：

[1] Shenyang Aerosp Univ, Sch Sci, Shenyang 110136, Peoples R China

[2] Jilin Univ, Inst Math, Changchun 130012, Peoples R China

[3] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2012年 / 30卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Stokes equations; Equal-order finite element pair; Finite volume method; Error estimate; GENERALIZED DIFFERENCE-METHODS; ELEMENT METHODS; COVOLUME METHOD; FLOW;

D O I：

10.4208/jcm.1206-m3843

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair (piecewise bilinear velocities and pressures) and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H-1 norm and the pressure in the L-2 norm. In addition, a second order optimal error estimate for the velocity in the L-2 norm is derived. Numerical experiments illustrating the theoretical results are included.

引用

页码：615 / 628

页数：14

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