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Applied Mathematics and Mechanics

, Volume 28, Issue 1, pp 27–35 | Cite as

Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations

  • Ma Fei-yao  (马飞遥)Email author
  • Ma Yi-chen  (马逸尘)
  • Wo Wei-feng  (沃维丰)
Article

Abstract

Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.

Key words

Navier-Stokes equations finite element method two-grid local parallel 

Chinese Library Classification

O241.82 

2000 Mathematics Subject Classification

65N30 65N55 

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References

  1. [1]
    Xu Jinchao. A novel two-grid method for semilinear equations[J]. SIAM J Sci Comput, 1994, 15(1):231–237.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Xu Jinchao. Two-grid discretization techniques for linear and nonlinear PDEs[J]. SIAM J Numer Anal, 1996, 33(5):1759–1777.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Xu Jinchao, Zhou Aihui. Local and parallel finite element algorithms based on two-grid discretizations[J]. Math Comp, 2000, 69(231):881–909.CrossRefMathSciNetGoogle Scholar
  4. [4]
    Xu Jinchao, Zhou Aihui. Local and parallel finite elment algorithms based on two-grid discretizations for nonlinear problems[J]. Adv Comp Math, 2001, 14(4):293–327.CrossRefMathSciNetGoogle Scholar
  5. [5]
    He Yinnian, Xu Jinchao, Zhou Aihui. Local and parallel finite element algorithms for the Stokes problem[J]. Numerische Mathematik, 2007, to be published.Google Scholar
  6. [6]
    Adams R. Sobolev space[M]. New York: Academic Press Inc, 1975.Google Scholar
  7. [7]
    Girault V, Raviart P A. Finite element methods for the Navier-Stokes equations: theory and algorithms[M]. Berlin: Springer-Verlag, 1986.Google Scholar
  8. [8]
    Ren Chunfeng, Ma Yichen. Two-grid error estimates for the stream function form of Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(7):773–782.MathSciNetGoogle Scholar
  9. [9]
    Ren Chunfeng, Ma Yichen, Ying Genjun. A two-grid method with backtracking technique for the Navier-Stokes equations[J]. Num Math J Chinese Uni, 2003, 25(3):193–204.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Ma Fei-yao  (马飞遥)
    • 1
    Email author
  • Ma Yi-chen  (马逸尘)
    • 1
  • Wo Wei-feng  (沃维丰)
    • 2
  1. 1.College of ScienceXi’an Jiaotong UniversityXi’anP. R. China
  2. 2.Center for Nonlinear StudiesNorthwest UniversityXi’anP. R. China

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