Navier-Stokes方程的一种并行两水平有限元方法

尚月强; 罗振东

doi:10.3879/j.issn.1000-0887.2010.11.008

Navier-Stokes方程的一种并行两水平有限元方法

doi: 10.3879/j.issn.1000-0887.2010.11.008

尚月强¹,
罗振东^1,2

贵州师范大学数学与计算机科学学院,贵阳 550001;

基金项目: 国家自然科学基金资助项目(11001061);贵州省科学技术基金资助项目(2008(2123))

详细信息

作者简介:
尚月强(1976- ),男,贵州人,副教授,博士(联系人.E-mail:yueqiangshang@gmail.com).

中图分类号: O241.82
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- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-10-11
- 刊出日期: 2010-11-15

A Parallel Two-Level Finite Element Method for the Navier-Stokes Equations

SHANG Yue-qiang¹,
LUO Zhen-dong^1,2

School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, P. R. China;
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China

摘要

摘要: 基于区域分解技巧,提出了一种求解定常Navier-Stokes方程的并行两水平有限元方法．该方法首先在一粗网格上求解Navier-Stokes方程,然后在细网格的子区域上并行求解粗网格解的残差方程,以校正粗网格解．该方法实现简单,通信需求少．使用有限元局部误差估计,推导了并行方法所得近似解的误差界,同时通过数值算例,验证了其高效性．
- Navier-Stokes方程 /
- 有限元方法 /
- 两水平方法 /
- 重叠型区域分解 /
- 并行算法
Abstract: Based on domain decomposition,a parallel two-level finite element method for the stationary Navier-Stokes equations was proposed and analyzed. The basic idea of the method was to first solve the Navier-Stokes equations on a coarse grid,then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations,error bounds of the approximate solution were derived. Numerical results were also given to illustrate the high efficiency of the method.
- Navier-Stokes equations /
- finite element /
- two-level method /
- overlapping domain decomposition /
- parallel algorithm

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参考文献(10)

[1]	HE Yin-nian, XU Jin-chao, ZHOU Ai-hui. Local and parallel finite element algorithms for the Navier-Stokes problem[J]. J Comput Math, 2006, 24(3): 227-238.
[2]	马飞遥, 马逸尘, 沃维丰. 基于二重网格的定常Navier-Stokes方程的局部和并行有限元算法[J]. 应用数学和力学, 2007, 28(1): 27-35.
[3]	Adams R. Sobolev Spaces[M].New York: Academic Press Inc, 1975.
[4]	Girault V， Raviart P A. Finite Element Methods for Navier-Stokes Equations—Theory and Algorithms[M].Berlin: Springer-Verlag， 1986.
[5]	HE Yin-nian, LI Jian. Convergence of three iterative methods based on finite element discretization for the stationary Navier-Stokes equations[J]. Comput Meth Appl Mech Engrg, 2009, 198: 1351-1359. doi: 10.1016/j.cma.2008.12.001
[6]	XU Jin-chao, ZHOU Ai-hui. Local and parallel finite element algorithms based on two-grid discretizations[J]. Math Comput, 2000, 69(231): 881-909.
[7]	SHANG Yue-qiang, HE Yin-nian. Parallel iterative finite element algorithms based on full domain partition for the stationary Navier-Stokes equations[J].Appl Numer Math, 2010, 60(7): 719-737. doi: 10.1016/j.apnum.2010.03.013
[8]	HE Yin-nian. A fully discrete stabilized finite element method for the time-dependent Navier-Stokes problem[J].IMA J Numer Anal, 2003, 23(4): 665-691. doi: 10.1093/imanum/23.4.665
[9]	HE Yin-nian. A two-level finite element Galerkin method for the nonstationary Navier-Stokes equations II: time discretization[J].J Comput Math, 2004, 22(1): 33-54.
[10]	Heywood J G, Rannacher R.Finite element approximation of the nonstationary Navier-Stokes problem I: regularity of solutions and second-order error estimates for spatial discretization[J]. SIAM J Numer Anal, 1982, 19(2): 275-311. doi: 10.1137/0719018