Communications in Mathematical Sciences

Volume 2 (2004)

Number 4

Multiscale Finite Element Methods for Nonlinear Problems and Their Applications

Pages: 553 – 589



Y. Efendiev

V. Ginting

T. Y. Hou


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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