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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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.|
|Subject Keywords:||multiscale, finite element, upscaling, nonlinear, elliptic, oversampling|
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|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.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||12 Oct 2011 17:02|
|Last Modified:||26 Dec 2012 14:15|
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