A novel L∞ image analysis for finite volume approximations of the Stokes problem

• Jian Li ^[1] ; Xin Zhao ^[1] ; Zhangxin Chen ^[2]
  1. [1] Baoji University of Arts and Sciences

     Baoji University of Arts and Sciences

     China

     
  2. [2] University of Calgary

     University of Calgary

     Canadá

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 279, Nº 1 ((1 May 2015)), 2015, págs. 97-105
• Idioma: inglés
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• Resumen

  • In this paper, a novel L∞ analysis for finite volume approximations of the Stokes problem is presented. Optimal order estimates in the L∞-norm for the velocity gradient and pressure of this problem are obtained by using new technical results. In particular, these optimal error estimates for the finite volume approximations are obtained without the presence of a usual logarithmic factor O(|logh|) for the stationary Stokes problem. Several numerical tests are performed to check these theoretical expectations.