American Institute of Mathematical Sciences

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September  2007, 6(3): 757-773. doi: 10.3934/cpaa.2007.6.757

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, China
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, China

Received  March 2006 Revised  August 2006 Published  June 2007

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.
Keywords: tensor product, two-scale discretization., localization, parallelization, Finite element.
Mathematics Subject Classification: Primary: 65N15, 65N30; Secondary: 65N55, 65N1.
Citation: Fang Liu, Aihui Zhou. Localizations and parallelizations for two-scale finite element discretizations. Communications on Pure and Applied Analysis, 2007, 6 (3) : 757-773. doi: 10.3934/cpaa.2007.6.757
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