Conca, Carlos; Orive, Rafael; Vanninathan, Muthusamy Bloch approximation in homogenization and applications. (English) Zbl 1010.35004 SIAM J. Math. Anal. 33, No. 5, 1166-1198 (2002). 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. Reviewer: Marco Codegone (Torino) Cited in 1 ReviewCited in 44 Documents 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 Keywords:periodically oscillating coefficients; Bloch waves; correctors PDFBibTeX XMLCite \textit{C. Conca} et al., SIAM J. Math. Anal. 33, No. 5, 1166--1198 (2002; Zbl 1010.35004) Full Text: DOI