Published December 2004
| Published
Journal Article
Open
Multiscale Finite Element Methods for Nonlinear Problems and their Applications
- Creators
-
Efendiev, Y.
- Hou, T. Y.
- Ginting, V.
Chicago
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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.
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.Attached Files
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Additional details
- Eprint ID
- 27179
- Resolver ID
- CaltechAUTHORS:20111012-093928630
- NSF
- DMS-0327713
- NSF
- EIA-0218229
- NSF
- ACI-0204932
- Created
-
2011-10-12Created from EPrint's datestamp field
- Updated
-
2019-10-03Created from EPrint's last_modified field
- Other Numbering System Name
- AMS Classification number
- Other Numbering System Identifier
- 65N99