Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (7): 783-793.

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A NONLINEAR GALERKIN/PETROV-LEAST SQUARES MIXED ELEMENT METHOD FOR THE STATIONARY NAVIER-STOKES EQUATIONS

LUO Zhen-dong1,2, ZHU Jiang2, WANG Hui-jun2   

  1. 1. Department of Mathematics, Capital Normal University, Beijing 100037, P R China;
    2. ICCES, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, P R China
  • Received:2001-09-28 Revised:2003-03-30 Online:2002-07-18 Published:2002-07-18
  • Supported by:
    the National Natural Science Foundation of China(10071052,49776283);the Project of the Evolvement Plan of Science and Technology of Beijing Educational Council;the Project of the Plan of Hundreds Persons of Chinese Academy of Sciences;the Key Project Natural Cybernetics Study of Ninth Five-Year Plan of Chinese Academy of Sciences(K2952-51-434);the Project of Beijing Excellent Talent Special Foundation;the Municipal Science Foundation of Beijng

Abstract: A nonlinear Galerkin/Petrov-least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babu*lka-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the NGPLSME solution is proved in the case of sufficient viscosity (or small data).

2010 MSC Number: 

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