Generalized multiscale finite element method for elasticity equations

Tsz Shun Eric CHUNG Yalchin Efendiev Shubin Fu

TBD mathscidoc:1910.43474

GEM-International Journal on Geomathematics, 5, (2), 225-254, 2014.11
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter
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@inproceedings{tsz2014generalized,
  title={Generalized multiscale finite element method for elasticity equations},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Shubin Fu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180048549217003},
  booktitle={GEM-International Journal on Geomathematics},
  volume={5},
  number={2},
  pages={225-254},
  year={2014},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Shubin Fu. Generalized multiscale finite element method for elasticity equations. 2014. Vol. 5. In GEM-International Journal on Geomathematics. pp.225-254. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180048549217003.
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