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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (11): 1429-1438.doi: https://doi.org/10.1007/s10483-010-1373-7

• Articles • 上一篇    下一篇

A parallel two-level finite element method for the Navier-Stokes equations

尚月强1 罗振东1,2   

  1. 1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, P. R. China;
    2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China
  • 收稿日期:2010-02-16 修回日期:2010-09-10 出版日期:2010-11-01 发布日期:2010-11-01

A parallel two-level finite element method for the Navier-Stokes equations

 SHANG Yue-Qiang1, LUO Zhen-Dong1,2   

  1. 1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, P. R. China;
    2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China
  • Received:2010-02-16 Revised:2010-09-10 Online:2010-11-01 Published:2010-11-01

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摘要： Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to 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 are derived. Numerical results are also given to illustrate the high efficiency of the method.

Abstract: Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to 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 are derived. Numerical results are also given to illustrate the high efficiency of the method.

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