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

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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

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.

2010 MSC Number: 

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