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A multiscale finite element method for elliptic problems in composite materials and porous media. (English) Zbl 0880.73065
We study a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving all the small scale features. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator. Our method is applicable to general multiple-scale problems without restrictive assumptions.

74S05 Finite element methods applied to problems in solid mechanics
74E30 Composite and mixture properties
74E05 Inhomogeneity in solid mechanics
76S05 Flows in porous media; filtration; seepage
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