Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 2, Number 4 (2004), 553-589.
Multiscale Finite Element Methods for Nonlinear Problems and Their Applications
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.
Commun. Math. Sci. Volume 2, Number 4 (2004), 553-589.
First available in Project Euclid: 3 March 2005
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Efendiev, Y.; Hou, T. Y.; Ginting, V. Multiscale Finite Element Methods for Nonlinear Problems and Their Applications. Commun. Math. Sci. 2 (2004), no. 4, 553--589. http://projecteuclid.org/euclid.cms/1109885498.