Localizations and parallelizations for two-scale finite element discretizations

Fang Liu; Aihui Zhou

doi:10.3934/cpaa.2007.6.757

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2007, Volume 6, Issue 3: 757-773. Doi: 10.3934/cpaa.2007.6.757

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Localizations and parallelizations for two-scale finite element discretizations

Fang Liu^1, and
Aihui Zhou^2,

1.
School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081
2.
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P.O.Box 2719

Received: March 2006

Revised: August 2006

Published: August 2007

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Abstract

Some local and parallel algorithms for two-scale finite element discretizations are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic boundary value problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on partially fine grids by some local procedure. A theoretical tool for analyzing these algorithms is some recent local error estimates for finite element approximations.

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Mathematics Subject Classification: Primary: 65N15, 65N30; Secondary: 65N55, 65N10.

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