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Analysis of the heterogeneous multiscale method for parabolic homogenization problems


Authors: Pingbing Ming and Pingwen Zhang
Journal: Math. Comp. 76 (2007), 153-177
MSC (2000): Primary 65N30, 35K05, 65N15
DOI: https://doi.org/10.1090/S0025-5718-06-01909-0
Published electronically: October 10, 2006
MathSciNet review: 2261016
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Abstract: The heterogeneous multiscale method (HMM) is applied to various parabolic problems with multiscale coefficients. These problems can be either linear or nonlinear. Optimal estimates are proved for the error between the HMM solution and the homogenized solution.


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Additional Information

Pingbing Ming
Affiliation: LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55 Zhong-Guan-Cun East Road, Beijing, 100080, People’s Republic of China
Email: mpb@lsec.cc.ac.cn

Pingwen Zhang
Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
Email: pzhang@pku.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-06-01909-0
Keywords: Heterogeneous multiscale method, parabolic homogenization problems, finite element methods
Received by editor(s): June 3, 2003
Received by editor(s) in revised form: December 6, 2005
Published electronically: October 10, 2006
Additional Notes: The first author was partially supported by the National Natural Science Foundation of China under the grant 10571172 and also supported by the National Basic Research Program under the grant 2005CB321704.
The second author was partially supported by National Natural Science Foundation of China for Distinguished Young Scholars 10225103 and also supported by the National Basic Research Program under the grant 2005CB321704.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.