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Article Contents

# Localizations and parallelizations for two-scale finite element discretizations

• 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.

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

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