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Bloch approximation in homogenization and applications. (English) Zbl 1010.35004

In a first part of this paper, the authors present a review of the classical problem of homogenization of elliptic operators with periodically oscillating coefficients. A new proof of weak convergence was furnished using Bloch wave decomposition. Following, the authors introduce the Bloch approximation, which provides energy norm approximation for the solution. Applications of this method are developed. The problem of correctors is treated, too. First- and second-order correctors yield an error estimate in the energy norm.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
35A25 Other special methods applied to PDEs
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