数学物理学报 ›› 2010, Vol. 30 ›› Issue (4): 1018-1029.

• 论文 • 上一篇    下一篇

非定常Navier-Stokes方程的质量集中各向异性非协调有限元逼近

石东洋1, 王慧敏1, 2   

  1. 1.郑州大学 数学系 郑州 450052|2.河南工程学院 数理科学系 郑州 450007
  • 收稿日期:2007-12-08 修回日期:2009-01-15 出版日期:2010-07-25 发布日期:2010-07-25
  • 基金资助:

    国家自然科学基金(10671184, 10971203)和河南省教育厅自然科学勘察计划项目(2009A110024)资助

The Lumped Mass Nonconforming Finite Element Approximation for the Nonstationary Navier-Stokes Equations on Anisotropic Meshes

 SHI Dong-Yang1, WANG Hui-Min1, 2   

  1. 1.Deparment of Mathematics, |Zhengzhou University, Zhengzhou 450052;
    2.Department of Mathematics and Physics, Henan Institute of Engineering, Zhengzhou |450007
  • Received:2007-12-08 Revised:2009-01-15 Online:2010-07-25 Published:2010-07-25
  • Supported by:

    国家自然科学基金(10671184, 10971203)和河南省教育厅自然科学勘察计划项目(2009A110024)资助

摘要:

该文将一个低阶Crouzeix-Raviart型非协调三角形元应用到非定常Navier-Stokes方程, 给出了其质量集中有限元逼近格式.在不需要传统Ritz-Volterra投影下,通过引入两个辅助有限元空间对边界进行估计的技巧,在各向异性网格下导出了速度的$L^2$模和能量模及压力的L2模的误差估计.

关键词: Navier-Stokes方程, 质量集中, 各向异性, 非协调元, 误差估计

Abstract:

In this paper, a low order Crouzeix-Raviart type nonconforming triangular element is applied to the nonstationary Navier-Stokes equations. The approximation scheme of the lumped mass finite element methods for the problem is proposed. Without using Ritz-Volterra projection, the error estimates are derived both in the L2-norm and the energy norm for velocity and the L2-norm for pressure on anisotropic meshes through the technique of introducing two auxiliary finite element spaces to the boundary estimate.

Key words: Navier-Stokes equations, Lumped mass, Anisotropic meshes, Nonconforming finite element, Error estimate

中图分类号: 

  • 65N15