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Multiscale Finite Element Methods for Nonlinear Problems and their Applications

Efendiev, Y. and Hou, T. Y. 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.

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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.

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Efendiev, Y.0000-0001-9626-303X
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.
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Subject Keywords:multiscale, finite element, upscaling, nonlinear, elliptic, oversampling
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AMS Classification number 65N99
Issue or Number:4
Record Number:CaltechAUTHORS:20111012-093928630
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27179
Deposited By: Ruth Sustaita
Deposited On:12 Oct 2011 17:02
Last Modified:03 Oct 2019 03:21

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