On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators

Abstract : We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the equation can be incomplete. A theoretical foundation of the approach in the limit of infinitely small oscillations of the coefficients is provided, using the classical theory of homogenization. We present a comprehensive study of the implementation aspects of our method, and a set of numerical tests and comparisons that show the potential practical interest of the approach. The approach detailed in this article improves on an earlier version briefly presented in [C. Le Bris, F. Legoll and K. Li, C. R. Acad. Sci. Paris 2013].
Type de document :
Article dans une revue
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018
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https://hal.archives-ouvertes.fr/hal-01420187
Contributeur : Frederic Legoll <>
Soumis le : mardi 20 décembre 2016 - 12:50:57
Dernière modification le : jeudi 14 septembre 2017 - 01:08:57

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  • HAL Id : hal-01420187, version 1
  • ARXIV : 1612.05807

Citation

Claude Le Bris, Frederic Legoll, Simon Lemaire. On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018. <hal-01420187>

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