Bloch approximation in homogenization and applications (Q2782976)

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.