一类Stokes方程的最小二乘混合元方法

顾海明; 羊丹平; 隋树林; 刘新民

一类Stokes方程的最小二乘混合元方法

1.
青岛化工学院计算机系, 青岛 266042;
2.
山东大学数学院, 济南 250100

基金项目: 国家教委博士点基金资助项目

详细信息

作者简介:
顾海明(1967~ ),男,博士,副教授.

中图分类号: O241.82
计量
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- 被引次数: 0
出版历程
- 收稿日期: 1998-09-01
- 修回日期: 2000-01-06
- 刊出日期: 2000-05-15

Least-Squares Mixed Finite Element Method for a Class of Stokes Equation

1.
Qingdao Institute of Chemical Technology, Qingdao 266042, P. R. China;
2.
Department of Mathematics, Shandong University, Jinan 250100, P. R. China

摘要

摘要: 对定常和非定常两种类型的Stokes方程建立了一类新的最小二乘混合元方法,并进行了分析,对定常的方程,采用了对u和σ的不同指标的有限元空间进行计算(LBB条件不需要),得到了最优的H¹和L²模估计.对非定常的方程,采用了传统的Raviart-Thomas混合元空间,得到了最优的L²模估计.
- 最小二乘 /
- 混合元 /
- 误差估计
Abstract: A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal L² and H¹ -error estimates are derived under the standard regularity assumption on the finite element partition(the LBB-condition is not required). For the evolutionary equation, optimal L² estimates are derived under the conventional Raviart-Thomas spaces.
- Least squares /
- mixed finite element method /
- error estimates

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参考文献(11)

[1]	Aziz A K,Kellogg R B,Stephens A B.Least-squares methods for elliptic systems[J].Math Comp,1985,44:53～70.
[2]	Bramble J H,Nitsche J A.A generalized Ritz-least-squares method for Dirichlet problems[J].SIAM J Numer Anal,1973,10:81～93.
[3]	Raviart R A,Thomas J M.A mixed finite element method for 2nd elliptic problems[A].In:Math Aspects of the FEM,Lecture Notes in Math[C].Vol,606,Berlin and New York:Springer-Verlag,1977,292～315.
[4]	Brezzi F.On the existence,uniqueness and approximation of saddle point problems arising from Lagrange multipliers[J].RAIRO Anal Numer,1974,8:129～151.
[5]	Carey G F,Oden J T.Finite Element:A Second Course[M].VolⅡ.Englewood Cliffs N J:Printice-Hall,1983.
[6]	Pehlivanov A I,Carey G F,Lazarov R D.Least-squares mixed finite element for second-order elliptic problems[J].SIAM J Numer Anal,1994,5:1368～1377.
[7]	Pehlivanov A I,Carey G F.Error estimates for least-squares mixed finite elements[J].Math Model Numer Anal,1994,5:517～537.
[8]	Cai Z,Lazarov R,Nanteuffel T A,et al.First-order system least squares for second-order partial differential equations Part Ⅰ[J].SIAM J Numer Anal,1994,6:1785～1799.
[9]	Johnson C,Thomee V.Error estimates for some mixed finite element methods for parabolic type problems[J].RAIRO Anal Numer,1981,15:41～78.
[10]	Girault V,Raviart P A.Finite element approximation of the Naviart-Stokes equations[A].In:Lecture Notes in Mathematics[C].Vol 749,Berlin,Heidelberg,New York:Springer-Verlag,1979.
[11]	Wheeler M F.A priorierror estimates for Galerkin approximations to parabolic partial differential equations[J].SIAM J Numer Anal,1973,4:723～758.