Multiscale Finite Element Methods for Nonlinear Problems and Their Applications
Efendiev, Y. ; Hou, T. Y. ; Ginting, V.
Commun. Math. Sci., Tome 2 (2004) no. 2, p. 553-589 / Harvested from Project Euclid
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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.
Publié le : 2004-12-14
Classification:  
@article{1109885498,
     author = {Efendiev, Y. and Hou, T. Y. and Ginting, V.},
     title = {Multiscale Finite Element Methods for Nonlinear Problems and Their Applications},
     journal = {Commun. Math. Sci.},
     volume = {2},
     number = {2},
     year = {2004},
     pages = { 553-589},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1109885498}
}

Efendiev, Y.; Hou, T. Y.; Ginting, V. Multiscale Finite Element Methods for Nonlinear Problems and Their Applications. Commun. Math. Sci., Tome 2 (2004) no. 2, pp.  553-589. http://gdmltest.u-ga.fr/item/1109885498/