Generalized Multiscale Finite Element Method for Elasticity Problem in Fractured Media
In this work, we consider the elasticity problem in fractured media. For the efficient numerical solution, we present a Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM is used for the construction of a coarse grid approximation of the problem by solution of the local spectral problems. We consider two types of the multiscale basis functions: (1) CG-GMsFEM with continuous multiscale basis functions and (2) DG-GMsFEM with discontinuous multiscale basis functions. The result of the numerical solution for the two-dimensional model problem is presented to show the performance of the presented multiscale method for fractured media. We compute error between the multiscale solution with the fine-scale solutions by choosing different numbers of multiscale basis functions.
KeywordsFractured media Elasticity problem Discontinuous Galerkin Multiscale method GMsFEM
This work is supported by the grant of the Russian Scientific Found (N 17-71-20055).
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