Local and parallel finite element algorithms for the stokes problem

Yinnian He; Jinchao Xu; Aihui Zhou; Jian Li

doi:10.1007/s00211-008-0141-2

Local and parallel finite element algorithms for the stokes problem

Yinnian He
, Jinchao Xu
, Aihui Zhou
, Jian Li

Research output: Contribution to journal › Article › peer-review

128 Scopus citations

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.

Original language	English (US)
Pages (from-to)	415-434
Number of pages	20
Journal	Numerische Mathematik
Volume	109
Issue number	3
DOIs	https://doi.org/10.1007/s00211-008-0141-2
State	Published - May 1 2008

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1007/s00211-008-0141-2

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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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AU - He, Yinnian

AU - Xu, Jinchao

AU - Zhou, Aihui

AU - Li, Jian

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N2 - 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.

AB - 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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Local and parallel finite element algorithms for the stokes problem

Abstract

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