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The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains

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Abstract

In this contribution we analyze a generalization of the heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains. The method was originally introduced by E and Engquist (Commun Math Sci 1(1):87–132, 2003) for homogenization problems in fixed domains. It is based on a standard finite element approach on the macroscale, where the stiffness matrix is computed by solving local cell problems on the microscale. A-posteriori error estimates are derived in L 2(Ω) by reformulating the problem into a discrete two-scale formulation (see also, Ohlberger in Multiscale Model Simul 4(1):88–114, 2005) and using duality methods afterwards. Numerical experiments are given in order to numerically evaluate the efficiency of the error estimate.

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  1. Institut für Numerische und Angewandte Mathematik, Einsteinstraße 62, 48149, Münster, Germany

    Patrick Henning & Mario Ohlberger

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  1. Patrick Henning
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  2. Mario Ohlberger
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Henning, P., Ohlberger, M. The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains. Numer. Math. 113, 601–629 (2009). https://doi.org/10.1007/s00211-009-0244-4

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