Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1331-1347.doi: 10.1016/S0252-9602(17)30076-0

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LOCAL AND PARALLEL FINITE ELEMENT METHOD FOR THE MIXED NAVIER-STOKES/DARCY MODEL WITH BEAVERS-JOSEPH INTERFACE CONDITIONS

Guangzhi DU1, Liyun ZUO2   

  1. 1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;
    2. School of Mathematical Sciences, University of Jinan, Jinan 250022, China
  • Received:2016-04-06 Revised:2016-11-09 Online:2017-10-25 Published:2017-10-25
  • Contact: Guangzhi DU,E-mail:guangzhidu@gmail.com E-mail:guangzhidu@gmail.com
  • Supported by:

    Supported by NSFC (11571274 and 11401466).

Abstract:

In this paper, we consider the mixed Navier-Stokes/Darcy model with Beavers-Joseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.

Key words: Navier-Stokes equations, Darcy's law, two-grid algorithm, Beavers-Joseph interface conditions, parallel finite element method

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