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Stokes方程的局部绝对稳定化有限元方法 被引量：3

A locally absolutely stabilized finite element method for the Stokes problem
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摘要 对于Stokes方程求解问题,作者提出了局部绝对稳定有限元方法.该方法可以看成是Kechkar和Silvester方法从线性/常数元到任意混合元的推广,也可以看成是Douglas和Wang整体绝对稳定化有限元方法的局部稳定化改进. A locally absolutely stabilized finite element mathod for the Stokes problem is presented in this paper. This new method can be seen as an extension of Kechker and Silvesters＇ method from linear/constant elements to any mixed elements, also can been regarded as a locally stabilized modification of Douglas and Wangs method.
作者 祁瑞生 冯民富 刘丹
机构地区 四川大学数学学院
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第3期436-440,共5页 Journal of Sichuan University(Natural Science Edition)
基金 四川省科技攻关课题(05GG006-006-2)
关键词 局部绝对稳定有限元法 宏元 跳跃项 locally absolutely stabilized finite element method,macro element, jump term
分类号 O241.82 [理学—计算数学]
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参考文献7

  • 1Brezzi F,Pitkranta J.On the stabilization of finite element approximations of the Stokes problem[C]∥Hackbusch W.Efficient solutions of elliptic systems.Braunschweig:Vieweg,1984,10:11.
  • 2Hughes T J R,Franca L P.A new finite element formulation for CFD:VII.the Stokes problem with various well-posed boundary conditions:symmetric formulations that converge for all velocity/pressure spaces[J].Comput Methods Appl.Mech Engrg,1987,65:85.
  • 3Douglas Jr J,Wang J.An absolutely stabilized finite element methods for Stokes problem[J].Math Comp,1989,52:495.
  • 4Kechkar N,Sivester D.Analysis of locally stabilized mixed finite element methods for the Stokes problem[J].Math Comp,1992,58:1.
  • 5Girault V,Raviart P A.Finite element methods for Navier-Stokes equations:theory and algorithms[M].Berlin-Heidelberg:Springer-Verlag,1986.
  • 6P Clément.Approximation by finite elements using local regularization[J].RAIRO Sér Rouge,1975,8:77.
  • 7Sterberg R.Analysis of mixed finite element methods for the Stokes problem:a unified approach[J].Math Comp,1984,42:9.

同被引文献46

  • 1Araya R, Barrenechea G and Valentin F. Stabilized finite element methods based on multiscale enrichment for the Stokes problem. SIAM J.Numer. Anal., 2006, 44(1): 322-348.
  • 2Arnold D N, Brezzi F and Fortin M. A stable finite dement for the Stokes equations. Calcolo, 2001, 21: 843-856.
  • 3Baiocchi C and Brezzi F. Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S). Comput. Methods Appl. Mech. Engrg, 1993, 105: 125-141.
  • 4Burman E. and Hansbo P. Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. Numerical Methods for Partial Differential Equation, 2005, 21(5): 986-997.
  • 5Barrenechea G and Valentin F. An unusual stabilized finite element method for a generalized Stokes problem, Numer. Math., 2002, 92: 653-677.
  • 6Blasco J and Codina R. Spaces and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations. Applied Numerical Mathematics, 2001, 38: 475-497.
  • 7Bochev P, Cai Z, Manteuffel T A and Mccormick S F. Analysis of velocity-flux first-order system least-square principles for the Navier-Stokes equations. SIAM. J. Numer. Anal., 1998, 35(3): 990-1009.
  • 8Bochev P and Gunzburger M D. A locally conservative least-squres method for Darcy flows. Commun. Numer. Meth. Engng, 2008, 24: 97-110.
  • 9Brezzi F, Bristeau M O, Franca L P, Mallet M and Roge G. A relationship between stabilized finite element methods and the Galerkin method with bubble functions. Comput. Mech. Appl. Mech. Engrg, 1992, 96(1): 117-129.
  • 10Burman E. Pressure projection stabilization for Galerkin approximations of Stokes' and Darcy' problem. Numerical Methods for Partial Differential Equation, 2008, 24(1): 127-143.

引证文献3

四川大学学报（自然科学版）
2010年 第3期

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