Numerische Mathematik

, Volume 109, Issue 3, pp 415-434

First online:

Local and parallel finite element algorithms for the stokes problem

  • Yinnian HeAffiliated withFaculty of Science, Xi’an Jiaotong University
  • , Jinchao XuAffiliated withLaboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking UniversityDepartment of Mathematics, Pennsylvania State University Email author 
  • , Aihui ZhouAffiliated withLSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
  • , Jian LiAffiliated withFaculty of Science, Xi’an Jiaotong University

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Based on two-grid discretizations, some local and parallel finite element algorithms for the Stokes problem are proposed and analyzed in this paper. These algorithms are motivated by the observation that for a solution to the Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. One technical tool for the analysis is some local a priori estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids.

Mathematics Subject Classification (2000)

65N15 65N30 76M10 76D07