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Spectral approach to homogenization of an elliptic operator periodic in some directions

Renata Bunoiu 1 Giuseppe Cardone 2 Tatiana Suslina 3
1 LMAM - Laboratoire de Mathématiques et Applications de Metz
2 Dipartimento di Ingegneria [Benevento]
3 SPbU - St Petersburg State University
Abstract : We study a homogenization problem for a family of elliptic differential operators whose coefficients are periodic in one direction. We use the spectral approach and we prove a norm convergence result for the generalized resolvent of the operator under study. The main tools used are the Floquet-Bloch decomposition and the perturbation theory.
Keywords : Floquet–Bloch decomposition perturbation theory spectral theory homogenization error estimates
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https://hal.inria.fr/hal-01283631
Contributor : Renata Bunoiu <>
Submitted on : Saturday, March 5, 2016 - 8:05:15 PM
Last modification on : Friday, July 9, 2021 - 11:30:45 AM

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Renata Bunoiu, Giuseppe Cardone, Tatiana Suslina. Spectral approach to homogenization of an elliptic operator periodic in some directions. Mathematical Methods in the Applied Sciences, Wiley, 2011, 34 (9), pp.1075-1096. ⟨10.1002/mma.1424⟩. ⟨hal-01283631⟩

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