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Constraint Energy Minimizing Generalized Multiscale Finite Element Method in the Mixed Formulation. (arXiv:1705.05959v1 [math.NA])
来源于:arXiv
This paper presents a novel mass-conservative mixed multiscale method for
solving flow equations in heterogeneous porous media. The media properties (the
permeability) contain multiple scales and high contrast. The proposed method
solves the flow equation in a mixed formulation on a coarse grid by
constructing multiscale basis functions. The resulting velocity field is mass
conservative on the fine grid. Our main goal is to obtain first-order
convergence in terms of the mesh size which is independent of local contrast.
This is achieved, first, by constructing some auxiliary spaces, which contain
global information that can not be localized, in general. This is built on our
previous work on the Generalized Multiscale Finite Element Method (GMsFEM). In
the auxiliary space, multiscale basis functions corresponding to small
(contrast-dependent) eigenvalues are selected. These basis functions represent
the high-conductivity channels (which connect the boundaries of a coarse
block). Next, we 查看全文>>