Reduction of the Resonance Error - Part 1: Approximation of Homogenized Coefficients

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 ε/η, where η is a typical macroscopic lengthscale and ε 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.