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Multiscale Finite Element Methods for Nonlinear Problems and their Applications

Efendiev, Y. and Hou, T. and Ginting, V. (2004) Multiscale Finite Element Methods for Nonlinear Problems and their Applications. Communications in Mathematical Sciences , 2 (4). pp. 553-589. ISSN 1539-6746. http://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630

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Abstract

In this paper we propose a generalization of multiscale finite element methods (Ms-FEM) to nonlinear problems. We study the convergence of the proposed method for nonlinear elliptic equations and propose an oversampling technique. Numerical examples demonstrate that the over-sampling technique greatly reduces the error. The application of MsFEM to porous media flows is considered. Finally, we describe further generalizations of MsFEM to nonlinear time-dependent equations and discuss the convergence of the method for various kinds of heterogeneities.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cms/1109885498PublisherUNSPECIFIED
Additional Information:© 2004 International Press. Received: June 22, 2004; accepted (in revised version): September 28, 2004. Communicated by Shi Jin. The research of Y. E. is partially supported by NSF grants DMS-0327713 and EIA-0218229. The research of T.Y.H. is partially supported by the NSF ITR grant ACI-0204932. We would like to acknowledge anonymous reviewers for their helpful comments which helped to improve the quality of the paper.
Funders:
Funding AgencyGrant Number
NSFDMS-0327713
NSFEIA-0218229
NSF-ITRACI-0204932
Subject Keywords:multiscale, finite element, upscaling, nonlinear, elliptic, oversampling
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Other Numbering System NameOther Numbering System ID
AMS Classification number 65N99
Record Number:CaltechAUTHORS:20111012-093928630
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630
Official Citation:Multiscale Finite Element Methods for Nonlinear Problems and Their Applications Y. Efendiev, V. Ginting and T. Y. Hou; 553-589
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27179
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Oct 2011 17:02
Last Modified:26 Dec 2012 14:15

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