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A mixed multiscale finite element method for elliptic problems with oscillating coefficients

Chen, Zhiming and Hou, Thomas Y. (2002) A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Mathematics of Computation, 72 (242). pp. 541-576. ISSN 0025-5718. https://resolver.caltech.edu/CaltechAUTHORS:CHEmc03

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Abstract

The recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large-scale structure of the solutions without resolving all the fine-scale structures. Motivated by the numerical simulation of flow transport in highly heterogeneous porous media, we propose a mixed multiscale finite element method with an over-sampling technique for solving second order elliptic equations with rapidly oscillating coefficients. The multiscale finite element bases are constructed by locally solving Neumann boundary value problems. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for flow transport in a porous medium with a random log-normal relative permeability to demonstrate the efficiency and accuracy of the proposed method.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.ams.org/journal-getitem?pii=S0025-5718-02-01441-2OtherUNSPECIFIED
Additional Information:© 2002 American Mathematical Society. Received by editor(s): March 21, 2000; received by editor(s) in revised form: July 10, 2000 and May 29, 2001. We wish to thank Dr. Yalchin R. Efendiev for many inspiring discussions and for providing us the code generating the log-normal permeability field. We would also like to thank Dr. Hector Ceniceros for his valuable comments on our original manuscript, and the referee for his careful reading and constructive comments. The first author was supported in part by China NSF under the grants 19771080 and 10025102 and by China MOS under the grant G1999032804. The second author was supported in part by NSF under the grant DMS-0073916 and by ARO under the grant DAAD19-99-1-0141.
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of China19771080
National Natural Science Foundation of China10025102
Ministry of Science and Technology (China)G1999032804
Issue or Number:242
Record Number:CaltechAUTHORS:CHEmc03
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:CHEmc03
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7271
Collection:CaltechAUTHORS
Deposited By: Lindsay Cleary
Deposited On:26 Feb 2007
Last Modified:21 Nov 2019 21:46

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