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December 2004 Multiscale Finite Element Methods for Nonlinear Problems and Their Applications
Y. Efendiev, V. Ginting, T. Y. Hou
Commun. Math. Sci. 2(4): 553-589 (December 2004).


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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Y. Efendiev. V. Ginting. T. Y. Hou. "Multiscale Finite Element Methods for Nonlinear Problems and Their Applications." Commun. Math. Sci. 2 (4) 553 - 589, December 2004.


Published: December 2004
First available in Project Euclid: 3 March 2005

zbMATH: 1083.65105
MathSciNet: MR2119929

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 4 • December 2004
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