定常的Navier-Stokes方程的非线性Galerkin混合元法及其后验估计

罗振东; 朱江

定常的Navier-Stokes方程的非线性Galerkin混合元法及其后验估计

罗振东^1,2,
朱江²

1.
首都师范大学数学系, 北京 100037;
2.
中国科学院大气物理研究所国际气候与环境科学研究中心, 北京 100029

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资助项目;北京市自然科学基金资助项目

详细信息

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:luozhd@mail.cnu.edu.cn).

中图分类号: O241.4
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- 被引次数: 0
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

A Nonlinear Galerkin Mixed Element Method and a Posteriori Error Estimator for the Stationary Navier-Stokes Equations

LUO Zhen-dong^1,2,
ZHU Jiang²

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

摘要: 提出了定常的Navier-Stokes方程的一种非线性Galerkin混合元法,并导出非线性Galerkin混合元解的存在性和误差估计及其后验误差估计.
- Navier-Stokes方程 /
- 非线性Galerkin混合元法 /
- 误差估计 /
- 后验误差估计
Abstract: A nonlinear Galerkin mixed element(NGME) method and a posteriori error estimator based on the method are established for the stationary Navier-Stokes equations. The esistence and error estimates of the NGME solution are first discussed,and then a posteriori error estimator based on the NGME method is derived.
- Navier-Stokes equation /
- nonlinear Galerkin mixed element method /
- error estimate /
- posteriori error estimator

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参考文献(33)

[1]	Foias C,Manley O P,Temam R. Modellization of the interaction of small and large eddies in two dimensional turbulent flows[J]. Math Mod Numer Anal,1988,22(1):93-114.
[2]	Marion M,Temam R. Nonlinear Galerkin methods[J]. SIAM J Numer Anal,1989,2(5):1139-1157.
[3]	Foias C,Jolly M,Kevrekidis I G,et al. Dissipativy of numerical schemes[J]. Nonlinearity,1991,4(4):591-613.
[4]	Devulder C,Marion M,Titi E. On the rate of convergence of nonlinear Galerkin methods[J]. Math Comp,1992,59(200):173-201.
[5]	Marion M,Temam R. Nonlinear Galerkin methods:the finite elements case[J]. Numer Math,1990,57(3):205-226.
[6]	Marion M,Xu J C. Error estimates on a new nonlinear Galerkin method based on two-grid finite elements[J]. SIAM J Numer Anal,1995,32(4):1170-1184.
[7]	Ait Ou Ammi A,Marion M. Nonlinear Galerkin methods and mixed finite element:two-grid algorithms for the Navier-Stokes equations[J]. Numer Math,1994,68(2):189-213.
[8]	Li K T,Zhou L. Finite element nonlinear Galerkin methods for penalty Navier-Stokes equations[J]. Math Numer Sinica,1995,17(4):360-380.
[9]	He Y,Li K T. Nonlinear Galerkin method and two-step method for the Navier-Stokes equations[J]. Inc Numer Methods P D Eq,1996,12(3):283-305.
[10]	Luo Z D,Wang L H. Nonlinear Galerkin mixed element methods for the non stationary conduction-convection problems(Ⅰ):The continuous-time case[J]. Chinese J Numer Math Appl,1998,20(4):71-94.
[11]	Luo Z D,Wang L H. Nonlinear Galerkin mixed element methods for the non stationary conduction-convection problems(Ⅱ):The backward one-step Euler fully discrete format[J]. Chinese J Numer Math Appl,1999,21(1):86-105.
[12]	罗振东,朱江,王会军. 定常的Navier-Stokes方程的非线性Galerkin/Petrov最小二乘混合元法[J]. 应用数学和力学,2002,23(7):697-708.
[13]	Li G C,He Y N. Convergence of nonlinear Galerkin finite element algorithm for the steady incompressible equations of the Navier-Stokes type[J]. Chinese J Comput Phys,1997,14(1):83-89.
[14]	Bank R E,Welfert B. A posteriori error estimates for the Stokes equations:A comparison[J]. Comput Methods Appl Mech Engrg,1990,82(3):323-340.
[15]	Bank R E,Welfert B. A posteriori error estimates for the Stokes problems[J]. SIAM J Numer Anal,1991,28(3):591-623.
[16]	Oden J T,Demkowicz L. h-p adaptive finite element methods in computational fluid dynamics[J]. Comput Methods Appl Mech Engrg,1991,89(1):11-40.
[17]	Padra C,Buscaglia G C,Dari E A. Adaptivity in steady incompressible Navier-Stokes equations using discontinuous pressure interpolates[A]. In:H Alder,J C Heinrich,S Lavanchy,et al Eds. Num Meth Eng Appl Sci,Part Ⅰ[C]. Barcelona:CIMNE,1992,267-276.
[18]	Wu J,Zhu J Z,Szmelter J,et al. Error estimation and adaptivity in Navier-Stokes incompressible flows[J]. Comput Mech,1990,6(2):259-270.
[19]	Verfürth R. A posteriori error estimators for the Stokes equations[J]. Numer Math,1989,55(3):309-325.
[20]	Verfürth R. A posteriori error estimators and adaptive mesh-refinement techniques for the Navier-Stokes equations[A]. In:M Gunzburger,R A Nicolaides Eds. Incompressible Computational Fluid Dynamics,Trends and Advances[C]. Cambridge:Cambridge University Press,1993,447-477.
[21]	Verfürth R. A posteriori error estimates for non-linear problems:Finite element discretizations of elliptic equations[J]. Math Comp,1994,62(206):445-475.
[22]	Oden J T,Wu W,Ainsworth M. An a posteriori error estimate for finite element approximations of the Navier-Stokes equations[J]. Comput Methods Appl Mech Engrg,1994,111(2):185-220.
[23]	Arnica D,Padra C. A posteriori error estimators for steady incompressible Navier-Stokes equations[J]. Inc Numer Methods P D Eq,1997,13(5):561-574.
[24]	Ervin V,Layton W,Maubach J. A posteriori error estimators for a two-level finite element method for the Navier-Stokes equations[J]. Inc Numer Methods P D Eq,1996,12(3):333-346.
[25]	Girault V,Raviart P A. Finite Element Approximations of the Navier-Stokes Equations,Theorem and Algorithms[M]. New York:Springer-Verlag,1986.
[26]	Temam R. Navier-Stokes Equations[M]. Amsterdam:North-Holland,1984.
[27]	Bernardi C,Raugel B. Analysis of some finite elements for the Stokes problem[J]. Math Comp,1985,44(169):71-79.
[28]	罗振东. 有限元混合法理论基础及其应用,发展与应用[M]. 济南:山东教育出版社,1996.
[29]	Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam:North-Holland,1978.
[30]	Luo Z D. The third order estimate of mixed finite element for the Navier-Stokes problems[J]. Chinese Quart J Math,1995,10(3):9-12.
[31]	Clément P. Approximation by finite element function using local regularization[J]. RAIRO,1975,R-2(1):77-84.
[32]	Layton W. A two level discretization method for the Navier-Stokes equations[J]. Comput Math Appl,1993,26(1):33-45.
[33]	Brezzi F,Fortin M. Mixed and Hybrid Finite Element Methods[M]. New York:Berlin,Heidelberg:Springer-Verlag,1991.