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

定常的磁流体力学方程的非线性Galerkin混合元法

罗振东 毛允魁 朱江

罗振东, 毛允魁, 朱江. 定常的磁流体力学方程的非线性Galerkin混合元法[J]. 应用数学和力学, 2006, 27(12): 1486-1496.
引用本文: 罗振东, 毛允魁, 朱江. 定常的磁流体力学方程的非线性Galerkin混合元法[J]. 应用数学和力学, 2006, 27(12): 1486-1496.
LUO Zhen-dong, MAO Yun-kui, ZHU Jiang. Nonlinear Galerkin Mixed Element Methods for the Stationary Incompressible Magnetohydrodynamics[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1486-1496.
Citation: LUO Zhen-dong, MAO Yun-kui, ZHU Jiang. Nonlinear Galerkin Mixed Element Methods for the Stationary Incompressible Magnetohydrodynamics[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1486-1496.

定常的磁流体力学方程的非线性Galerkin混合元法

基金项目: 国家自然科学基金资助项目(10471100;40437017)
详细信息
    作者简介:

    罗振东(1958- ),男,教授,博士生导师,研究方向:有限元方法及其应用(联系人.Tel:+86-10-51684751;Fax:+86-10-68902789;E-mail:zhdluo@bjtu.edu.cn).

  • 中图分类号: O241.4

Nonlinear Galerkin Mixed Element Methods for the Stationary Incompressible Magnetohydrodynamics

  • 摘要: 提出了定常的磁流体动力学方程的一种非线性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.
  • [1] Jackson J D.Classical Electrodynamics[M].New York:Wiley,1975.
    [2] Foias C,Manley O P,Temam R.Modelization of the interaction of small and large eddies in two dimensional turbulent flows[J].Math Model Numer Anal,1988,22(1):93—114.
    [3] Marion M,Temam R.Nonlinear Galerkin method[J].SIAM J Numer Anal,1989,2(5):1139—1157.
    [4] Foias C,Jolly M,Kevrekidis I G,et al.Dissipativy of numerical schemes[J].Nonlinearity,1991,4(4):591—613. doi: 10.1088/0951-7715/4/3/001
    [5] Devulder C,Marion M,Titi E.On the rate of convergence of nonlinear Galerkin methods[J].Math Comp,1992,59(200):173—201.
    [6] Marion M,Temam R.Nonlinear Galerkin methods: the finite elements case[J].Numer Math,1990,57(3):205—226. doi: 10.1007/BF01386407
    [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. doi: 10.1007/s002110050056
    [8] Li K T,Zhou L.Finite element nonlinear Galerkin methods for penalty Navier-Stokes equations[J].Math Numerica Sinica,1995,17(4):360—380.
    [9] 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.
    [10] 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.
    [11] Adams R A.Sobolev space[M].New York:Academic Press,1975.
    [12] Gunzburger M D,Meir A J,Peterson J S.On the existence,uniqueness,and finite element approximation of solution of the equation of stationary,incompressible magnetohydrodynamics[J].Math Comp,1991,56(194):523—563. doi: 10.1090/S0025-5718-1991-1066834-0
    [13] Ciarlet P G.The Finite Element Method for Elliptic Problems[M]. Amsterdam:North-Holland,1978.
    [14] Bernardi C,Raugel B. Analysis of some finite elements for the Stokes problem[J].Math Comp,1985,44(169):71—79. doi: 10.1090/S0025-5718-1985-0771031-7
    [15] Wiedmer M.Finite element approximation for equation of magnetohydrodynamics[J].Math Comp,1999,69(229):83—101. doi: 10.1090/S0025-5718-99-01146-1
    [16] 罗振东.混合有限元法基础及其应用[M].北京:科学出版社,2006.
    [17] Girault V,Raviart P A.Finite Element Approximations of the Navier-Stokes Equations, Theorem and Algorithms[M].New York:Springer-Verlag,1986.
    [18] 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[J].应用数学和力学,2002,23(10):1061—1072.
    [19] 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. doi: 10.1016/0045-7825(90)90170-Q
    [20] Temam R.Navier-Stokes Equations[M].Amsterdam:North-Holland,1984.
  • 加载中
计量
  • 文章访问数:  2800
  • HTML全文浏览量:  128
  • PDF下载量:  761
  • 被引次数: 0
出版历程
  • 收稿日期:  2005-03-01
  • 修回日期:  2006-07-27
  • 刊出日期:  2006-12-15

目录

    /

    返回文章
    返回