Analysis of the heterogeneous multiscale method for elliptic homogenization problems

E, Weinan¹ ; Ming, Pingbing² ; Zhang, Pingwen³

¹Department of Mathematics and PACM, Princeton University, Princeton, New Jersey 08544 and School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
²No. 55, Zhong-Guan-Cun East Road, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
³School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China

Journal of the American Mathematical Society, Tome 18 (2005) no. 1, pp. 121-156

Résumé

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.

Détail

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

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