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Generalized Multiscale Finite Element Method for Elasticity Problem in Fractured Media

  • V. AlekseevEmail author
  • A. Tyrylgin
  • M. Vasilyeva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

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.

Keywords

Fractured media Elasticity problem Discontinuous Galerkin Multiscale method GMsFEM 

Notes

Acknowledgments

This work is supported by the grant of the Russian Scientific Found (N 17-71-20055).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Multiscale Model Reduction LaboratoryNorth-Eastern Federal UniversityYakutskRussia
  2. 2.Institute for Scientific ComputationTexas A&M UniversityCollege StationUSA

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