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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2018

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

Résumé

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].

Dates et versions

hal-01420187 , version 1 (20-12-2016)

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Citer

Claude Le Bris, Frédéric 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, 2018, 24 (4), pp.1345-1380. ⟨10.1051/cocv/2017061⟩. ⟨hal-01420187⟩
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