# Reduction of the resonance error. Part 1: Approximation of homogenized coefficients

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1 SIMPAF - SImulations and Modeling for PArticles and Fluids LPP - Laboratoire Paul Painlevé, Inria Lille - Nord Europe

Abstract : This paper is concerned with the approximation of effective coefficients in homogenization of linear elliptic equations. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio $\epsilon-\eta$, where $\eta$ is a typical macroscopic lengthscale and $\epsilon$ is the typical size of the heterogeneities. In the present work, we propose an alternative for the computation of homogenized coefficients or more generally a modified cell-problem, which is a first brick in the design of effective numerical homogenization methods. We show that this approach drastically reduces the resonance error in some standard cases.

Autor: Antoine Gloria -

Fuente: https://hal.archives-ouvertes.fr/

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