Local and parallel finite element algorithms for the stokes problem |
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| Authors: | Yinnian He Jinchao Xu Aihui Zhou Jian Li |
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| Institution: | (1) Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China;(2) Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China;(3) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;(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 |
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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.
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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| Keywords: | 65N15 65N30 76M10 76D07 |
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