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Pré-Publication, Document De Travail Année : 2014

Reduction of the resonance error in numerical homogenization II: correctors, extrapolation, and spectral theory

Résumé

This paper is the companion article of [Gloria, M3AS, 21 (2011), No. 3, pp 1601-1630]. 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 $\e/\rho$, where $\rho$ is a typical macroscopic lengthscale and $\e$ is the typical size of the heterogeneities. In the present work, we make a systematic use of regularization and extrapolation to reduce this resonance error at the level of the approximation of homogenized coefficients and correctors. We quantify this reduction in the periodic case and in the case of Poisson random inclusions. We also report on a systematic numerical study in dimension 2, which demonstrates the efficiency of the method and the sharpness of the analysis. Last, we combine this approach to numerical homogenization methods, prove the asymptotic consistency in the case of locally stationary ergodic symmetric coefficients using spectral theory, and give quantitative estimates in the case of periodic coefficients.
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Dates et versions

hal-00933234 , version 1 (20-01-2014)
hal-00933234 , version 2 (03-09-2014)

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  • HAL Id : hal-00933234 , version 1

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Antoine Gloria, Zakaria Habibi. Reduction of the resonance error in numerical homogenization II: correctors, extrapolation, and spectral theory. 2014. ⟨hal-00933234v1⟩
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