留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

定常的Navier-Stokes方程的非线性Galerkin/Petrov最小二乘混合元法

罗振东 朱江 王会军

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): 697-706.
引用本文: 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): 697-706.
LUO Zhen-dong, ZHU Jiang, WANG Hui-jun. A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(7): 697-706.
Citation: LUO Zhen-dong, ZHU Jiang, WANG Hui-jun. A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(7): 697-706.

定常的Navier-Stokes方程的非线性Galerkin/Petrov最小二乘混合元法

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);北京市优秀人才工程专项经费资助项目;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,汉族,教授,博士生导师,博士,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

A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations

  • 摘要: 给出定常的Navier-Stokes方程的一种非线性Galerkin/Petrov最小二乘混合元法,该方法是将余量形式的Petrov最小二乘方法与非线性Galerkin混合元结合起来,使得速度和压力的混合元空间无需满足离散的Babu ka-Brezzi稳定性条件,从而使得它们的有限元空间可以任意选择。并证明该方法的解的存在唯一性和收敛性。
  • [1] Foias C,Manley O P,Temam R.Modelization of the interaction of small and large eddies in two dimensional turbulent flows[J].Math Mod Numer Anal,1988,22(2):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.Dissipativity of numerical schemes[J].Nonlinearity,1991,4(4):591-613.
    [4] Devulder C,Marion M,Titi E.On therate of convergence of nonlinear Galerkin methods[J].Math Comp,1992,59(200):173-201.
    [5] Marion M,Temam R.Nonlinear Galerkin methods:the finite elementcase[J].Numer Math,1990,57(3):205-226.
    [6] Marion M,Xu J C.Errorestimates on a new nonlinear Galer kinmeth od 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 elements:two-grid algorithms for the Navier-Stokes equations[J].Numer Math,1994,68(2):189-213.
    [8] LI Kai-tai,Zhou L.Finite element nonlinear Galerkin methods for penalty Navier-Stokes equations[J].Math Numer Sinica,1995,17(4):360-380.
    [9] LUO Zhen-dong,Wang L H.Nonlinear Galerkin mixed element methods for the nonstationary conduction-convection problems(Ⅰ):The continuous-time case[J].Mathematica Numerica Sinica,1998,20(3):283-304.
    [10] LUO Zhen-dong,Wang L H.Nonlinear Galerkin mixed element methods for the nonstationary conduction-convection problems(Ⅱ):The backward one-step Euler fully discrete format[J].Mathematica Numerica Sinica,1998,20[STBZ](4):90-108.
    [11] Girault V,Raviart P A.Finite Element Approximations of the Navier-Stokes Equations:Theorem and Algorithms[M].New York:Springer-Verlag,1986.
    [12] Temam R.Navier-Stokes Equations[M].New York,Amsterdam:North-Holland,1984.
    [13] France L P,Hughes T J.Two classes of mixed finite element methods[J].Comput Methods Appl Mech Engrg,1988,69(1):89-129.
    [14] Hughes T J,France L P,Balestra M.A new finite element formulation for computational fluid dynamics (Ⅴ):Circumventing the Bubuka-Brezzi condition:Astable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolation[J].Comput Methods Appl Mech Engrg,1986,(1):85-99.
    [15] Hughes T J,France L P.A new finite element formulation for computations fluid dynamics (Ⅶ):The Stokes problem with various well posed boundary conditions,symmetric formulations that converge for all velocity pressurespace[J].Comput Methods Appl Mech Engrg,1987,65(1):85-96.
    [16] Brezzi F,Douglas Jr J.Stabilized mixed method for the Stokes problem[J].Numer Math,1988,53(2):225-235.
    [17] Douglas Jr J,Wang J P.An absolutely stability finite element method for the stokes problem[J].Math Comp,1989,52(186):495-508.
    [18] Houghes T J,Tezduyar T E.Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations [J].Comput Methods Appl Mech Engrg,1984,45(3):217-284.
    [19] Johson C,Saranen J.Stremline diffusion methods for the incompre ssible Euler and Navier-Stokes equations[J].Math Comp,1986,47(175):1-18.
    [20] Hansbo P,Szepessy A.Avelocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations[J].Comput Methods Appl Mech Engrg,1990,84(2):175-192.
    [21] Zhou T X,Feng M F,Xiong H X.A new approach to stability of finite elements under divergence constraints[J].J Comput Math,1992,1 0(1):1-15.
    [22] Zhou T X,Feng M F.A least squares Petrov-Galerkin finite element method for the stationary Navier-Stokes equations[J].Math Comp,1993,60(202):531-543.
    [23] 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.
    [24] Ciarlet P G.The Finite Element Method for Elliptic Problems [M].Amsterdam:North-Holland,1978.
  • 加载中
计量
  • 文章访问数:  2538
  • HTML全文浏览量:  117
  • PDF下载量:  1215
  • 被引次数: 0
出版历程
  • 收稿日期:  2000-09-08
  • 修回日期:  2002-03-30
  • 刊出日期:  2002-07-15

目录

    /

    返回文章
    返回