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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Analysis of the heterogeneous multiscale method for elliptic homogenization problems
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by Weinan E, Pingbing Ming and Pingwen Zhang HTML | PDF
J. Amer. Math. Soc. 18 (2005), 121-156 Request permission

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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Additional Information
  • Weinan E
  • Affiliation: Department of Mathematics and PACM, Princeton University, Princeton, New Jersey 08544 and School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
  • MR Author ID: 214383
  • ORCID: 0000-0003-0272-9500
  • Email: weinan@Princeton.EDU
  • Pingbing Ming
  • Affiliation: No. 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
  • Email: mpb@lsec.cc.ac.cn
  • Pingwen Zhang
  • Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
  • Email: pzhang@pku.edu.cn
  • Received by editor(s): January 2, 2003
  • Published electronically: September 16, 2004
  • Additional Notes: The work of the first author was partially supported by ONR grant N00014-01-1-0674 and the National Natural Science Foundation of China through a Class B Award for Distinguished Young Scholars 10128102.
    The work of the second author was partially supported by the Special Funds for the Major State Basic Research Projects G1999032804 and was also supported by the National Natural Science Foundation of China 10201033.
    The work of the third author was partially supported by the Special Funds for the Major State Research Projects G1999032804 and the National Natural Science Foundation of China for Distinguished Young Scholars 10225103.
    We thank Bjorn Engquist for inspiring discussions on the topic studied here.
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 18 (2005), 121-156
  • MSC (2000): Primary 65N30, 74Q05; Secondary 74Q15, 65C30
  • DOI: https://doi.org/10.1090/S0894-0347-04-00469-2
  • MathSciNet review: 2114818