非定常Navier-Stokes方程的质量集中各向异性非协调有限元逼近

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

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.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-Min^{1, 2}

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/Abstract

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

石东洋, 王慧敏. 非定常Navier-Stokes方程的质量集中各向异性非协调有限元逼近[J]. 数学物理学报, 2010, 30(4): 1018-1029.

SHI Dong-Yang, WANG Hui-Min. The Lumped Mass Nonconforming Finite Element Approximation for the Nonstationary Navier-Stokes Equations on Anisotropic Meshes[J]. Acta mathematica scientia,Series A, 2010, 30(4): 1018-1029.

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