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Local and parallel finite element algorithms for the stokes problem

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinnian He & Jian Li

  2. Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Jinchao Xu

  3. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Jinchao Xu

  4. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, People’s Republic of China

    Aihui Zhou

Authors
  1. Yinnian He
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  2. Jinchao Xu
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  3. Aihui Zhou
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  4. Jian Li
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Corresponding author

Correspondence to Jinchao Xu.

Additional information

Y. He was partially subsidized by the NSF of China 10671154 and the National Basic Research Program under the grant 2005CB321703; A. Zhou was partially supported by the National Science Foundation of China under the grant 10425105 and the National Basic Research Program under the grant 2005CB321704; J. Li was partially supported by the NSF of China under the grant 10701001. J. Xu was partially supported by Alexander von Humboldt Research Award for Senior US Scientists, NSF DMS-0609727 and NSFC-10528102.

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He, Y., Xu, J., Zhou, A. et al. Local and parallel finite element algorithms for the stokes problem. Numer. Math. 109, 415–434 (2008). https://doi.org/10.1007/s00211-008-0141-2

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  • DOI: https://doi.org/10.1007/s00211-008-0141-2

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