数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 367-382.doi: 10.1016/S0252-9602(11)60238-5

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A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

石东洋1|任金城2|龚伟3   

  1. 1.Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China;2.Department of Mathematics, Shangqiu Normal University, Shangqiu 476000, China;3.Institute of Computational Mathematics, Academy of Mathematics and Systems Science,   |Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2007-09-07 修回日期:2010-02-27 出版日期:2011-03-20 发布日期:2011-03-20
  • 基金资助:

    The research is supported by NSF of China (10671184)

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

 SHI Dong-Yang1, REN Jin-Cheng2, GONG Wei3   

  1. 1.Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China;2.Department of Mathematics, Shangqiu Normal University, Shangqiu 476000, China;3.Institute of Computational Mathematics, Academy of Mathematics and Systems Science,   |Chinese Academy of Sciences, Beijing 100190, China
  • Received:2007-09-07 Revised:2010-02-27 Online:2011-03-20 Published:2011-03-20
  • Supported by:

    The research is supported by NSF of China (10671184)

摘要:

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

关键词: Stationary Navier-Stokes equations, nonconforming mixed finite element scheme, optimal order error estimates

Abstract:

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

Key words: Stationary Navier-Stokes equations, nonconforming mixed finite element scheme, optimal order error estimates

中图分类号: 

  • 65N15