Stokes问题基于泡函数的简化的稳定化混合元格式的收敛性

基金项目: 国家自然科学基金资助项目(10071052;49776283);北京市教委科技发展计划项目;中国科学院“百人计划“项目;中国科学院九五重点项目(K2952-51-434);北京市优秀人才专项经费;北京市自然科学基金资助项目

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

1.
Department of Mathematics, Capital Normal University, Beijing 100037, P R China;
2.
ICCES, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, P R China

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.
- Stokes问题 /
- 稳定化格式 /
- 混合元格式 /
- 误差分析
Abstract: Two simplified and stabilized mixed element formats for the Stokes problem are derived by bubble function,and their convergence,i. e.,error analysis,are proved. These formats can save more freedom degrees than other usual formats.
- Stokes problem /
- stabilized format /
- mixed element format /
- error analysis

[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.