Analysis of the heterogeneous multiscale method for elliptic homogenization problems

E, Weinan; Ming, Pingbing; Zhang, Pingwen

doi:10.1090/S0894-0347-04-00469-2

Analysis of the heterogeneous multiscale method for elliptic homogenization problems
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by Weinan E, Pingbing Ming and Pingwen Zhang

J. Amer. Math. Soc. 18 (2005), 121-156

DOI: https://doi.org/10.1090/S0894-0347-04-00469-2

Published electronically: September 16, 2004

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Abstract:

A comprehensive analysis is presented for the heterogeneous multiscale method (HMM for short) applied to various elliptic homogenization problems. These problems can be either linear or nonlinear, with deterministic or random coefficients. In most cases considered, optimal estimates are proved for the error between the HMM solutions and the homogenized solutions. Strategies for retrieving the microstructural information from the HMM solutions are discussed and analyzed.

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