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.
https://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 |
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| 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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| Funders: | | Funding Agency | Grant Number |
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| NSF | DMS-0327713 | | NSF | EIA-0218229 | | NSF | ACI-0204932 |
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| Subject Keywords: | multiscale, finite element, upscaling, nonlinear, elliptic, oversampling |
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| Other Numbering System: | | Other Numbering System Name | Other Numbering System ID |
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| AMS Classification number | 65N99 |
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| Issue or Number: | 4 |
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| Record Number: | CaltechAUTHORS:20111012-093928630 |
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| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630 |
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
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| ID Code: | 27179 |
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| Collection: | CaltechAUTHORS |
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| Deposited By: |
Ruth Sustaita
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| Deposited On: | 12 Oct 2011 17:02 |
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| Last Modified: | 03 Oct 2019 03:21 |
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