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Stokes问题基于泡函数的简化的稳定化混合元格式的收敛性

 引用本文: 罗振东, 朱江. Stokes问题基于泡函数的简化的稳定化混合元格式的收敛性[J]. 应用数学和力学, 2002, 23(10): 1073-1079.
LUO Zhen-dong, ZHU Jiang. Convergence of Simplified and Stabilized Mixed Element Formats Based on Bubble Function for the Stokes Problem[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1073-1079.
 Citation: LUO Zhen-dong, ZHU Jiang. Convergence of Simplified and Stabilized Mixed Element Formats Based on Bubble Function for the Stokes Problem[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1073-1079.

## Stokes问题基于泡函数的简化的稳定化混合元格式的收敛性

###### 作者简介:罗振东(1958- ),男,教授,博士,博士生导师,研究方向:有限元方法及其应用(E-mail:louzhd@mail.cnu.edu.cn).
• 中图分类号: O241.4

## Convergence of Simplified and Stabilized Mixed Element Formats Based on Bubble Function for the Stokes Problem

• 摘要: 利用泡函数导出Stokes问题的两种新的、简化的稳定化混合有限元格式.并证明这些格式与通常带泡函数的稳定化格式具有相同的收敛性,但是自由度可以大大减少.
•  [1] Brezzi F,Douglas J.Stabilized mixed methods for the Stokes problem[J].Numer Math,1988,53(2):225-235. [2] Fix G J,Gunzburger M D,Nicolaides R A.On mixed finite element methods for the first elliptic systems[J].Numer Math,1981,37(1):29-48. [3] Neittanmki P,Picard R.On finite element approximation of the gradient for the solution of Poisson equation[J].Numer Math,1981,37(3):333-337. [4] Pehlivanov A I,Carey G F.Error estimates for least-squares finite elements[J].M2AN,1994,28(5):499-516. [5] Russo A.A posteriori error estimators for the Stokes problems[J].Appl Math Lett,1995,8(1):1-4. [6] Zhou T X,Feng M F.A least squares Petrov-Galerkin finite element method for the staionary Navier-Stokes equations[J].Math Comp,1993,60(202):531-543. [7] 周天孝.基于鞍点问题对偶组合的有限元法及其理论[J].中国科学(E辑),1997,27(1):75-87. [8] Girault V,Raviart P A.Finite Element Approximations of the Navier-Stokes Equations,Theorem and Algorithms[M].Series in Computational Mathematics,Springer-Verlag,1986:1-210. [9] 罗振东.有限元混合法理论基础及其应用[M].济南:山东教育出版社,1996,32-144. [10] Brezzi F,Fortin M.Mixed and Hybrid Finite Element Methods[M].New York,Berlin,Heidelberg:Springer-Verlag,1991,1-190.

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##### 出版历程
• 收稿日期:  2000-08-30
• 修回日期:  2002-04-01
• 刊出日期:  2002-10-15

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