定常的磁流体动力学问题的Galerkin-Petrov最小二乘混合元方法

罗振东; 毛允魁; 朱江

定常的磁流体动力学问题的Galerkin-Petrov最小二乘混合元方法

北京交通大学理学院,北京 100044;2.中国科学院大气物理研究所,北京 100029

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,广西桂平人,教授,博士生导师(联系人.Tel:+86-10-51684751;Fax:+86-10-68902789;E-mail:zhdluo@bjtu.edu.cn).

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出版历程
- 收稿日期: 2005-03-01
- 修回日期: 2007-01-16
- 刊出日期: 2007-03-15

Petrov-Galerkin Least Squares Mixed Element Method for the Stationary Incompressible Magnetohydrodynamics

School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China;

摘要

摘要: 提出了定常的磁流体动力学方程的一种Galerkin-Petrov最小二乘混合元法，并导出Galerkin-Petrov最小二乘混合元解的存在性和误差估计．通过引入Galerkin-Petrov最小二乘混合有限元方法使得该方法的混合元空间之间的组合无需满足离散的Babuska-Brezzi稳定性条件，从而使得它们的混合有限元空间可以任意选取，并得到误差估计最优阶．
- 磁流体力学方程 /
- 混合元方法 /
- Galerkin-Petrov最小二乘法 /
- 误差估计
Abstract: A Galerkin-Petrov least squares mixed finite element method for the stationary magnetohy-drodynamics problems was introduced and the existence and error estimates of the Galerkin-Petrov least squares mixed finite element solution were derived.The combination among mixed finite element spaces of this method dose not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be arbitrarily chosen and the error estimates with optimal order could be obtained.
- equation of magnetohydrodynamics /
- mixed element method /
- Galerkin-Petrov-least squares method /
- error estimate

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参考文献(15)

[1]	Jackson J D.Classical Electrodynamics[M].New York: Wiley,1975.
[2]	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].Mathematics of Computation,1991,56(194):523-563. doi: 10.1090/S0025-5718-1991-1066834-0
[3]	Wiedmer M. Finite element approximation for equation of magnetohydrodynamics[J]. Mathematics of Computation,2000,69(229):83-101.
[4]	Girault V,Raviart P A.Finite Element Methods for Navier-Stokes Equations,Theory and Algorithms[M].Berlin: Springer-Verlag,1986.
[5]	Temam R.Navier-Stokes Equation[M].Amsterdam: North-holland, 1984.
[6]	France L P,Hughes T J. Two classes of mixed finite element methods[J].Computer Methods in Applied Mechanics and Engineering,1988,69(1):89-129. doi: 10.1016/0045-7825(88)90168-5
[7]	Hughes T J, France L P, Balestra M. A new finite element formulation for computational fluid dynamics, V.Circumventing the Babuka-Brezzi condition: A stable Petrov-Galerkin formulations of stokes problem accommodating equal-order interpolation[J].Computer Methods in Applied Mechanics and Engineering,1986,59(1):85-99. doi: 10.1016/0045-7825(86)90025-3
[8]	Hughes T J, France L P.A new finite element formulation for computational fluid dynamics, VII. The stokes problem with various well posed boundary condition, symmetric formulations that converge for all velocity pressure space[J].Computer Methods in Applied Mechanics and Engineering,1987,65(2): 85-96. doi: 10.1016/0045-7825(87)90184-8
[9]	Brezzi F, Douglas Jr J. Stabilized mixed method for the Stokes problem[J]. Numerische Mathematik,1988,53(2):225-235. doi: 10.1007/BF01395886
[10]	Douglas Jr J,Wang J P. An absolutely stabilized finite element method for the Stokes problem[J]. Math Comp,1989,52(186):495-508. doi: 10.1090/S0025-5718-1989-0958871-X
[11]	Hughes T J, Tezduyar T E. Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equation[J].Computer Methods in Applied Mechanics and Engineering,1984,45(3):217-284. doi: 10.1016/0045-7825(84)90157-9
[12]	Johson C, Saranen J. Streamline diffusion methods for the incompressible Euler and Navier-Stokes equation[J].Mathematics of Computation,1986,47(175):1-18. doi: 10.1090/S0025-5718-1986-0842120-4
[13]	Ciarlet P G.The Finite Element Method for Elliptic Problem[M].Amsterdam:North-Holland, 1978.
[14]	罗振东. 混合有限元法基础及其应用[M]. 北京: 科学出版社, 2006.
[15]	Zhou T X, Feng M F. A least squares Petrov-Galerkin finite element method for the stationary Navier-Stokes equations[J].Mathematics of Computation,1993,60(202):531-543. doi: 10.1090/S0025-5718-1993-1164127-6

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定常的磁流体动力学问题的Galerkin-Petrov最小二乘混合元方法

作者简介:
罗振东(1958- ),男,广西桂平人,教授,博士生导师(联系人.Tel:+86-10-51684751;Fax:+86-10-68902789;E-mail:zhdluo@bjtu.edu.cn).

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Petrov-Galerkin Least Squares Mixed Element Method for the Stationary Incompressible Magnetohydrodynamics

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留言板

定常的磁流体动力学问题的Galerkin-Petrov最小二乘混合元方法

作者简介: 罗振东(1958- ),男,广西桂平人,教授,博士生导师(联系人.Tel:+86-10-51684751;Fax:+86-10-68902789;E-mail:zhdluo@bjtu.edu.cn).

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出版历程

Petrov-Galerkin Least Squares Mixed Element Method for the Stationary Incompressible Magnetohydrodynamics

计量

出版历程

目录

作者简介:
罗振东(1958- ),男,广西桂平人,教授,博士生导师(联系人.Tel:+86-10-51684751;Fax:+86-10-68902789;E-mail:zhdluo@bjtu.edu.cn).