Mixed generalized multiscale finite element methods and applications

Tsz Shun Eric CHUNG Yalchin Efendiev Chak Shing Lee

Numerical Analysis and Scientific Computing mathscidoc:1910.43464

Multiscale Modeling & Simulation, 13, (1), 338-366, 2015.3
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of
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@inproceedings{tsz2015mixed,
  title={Mixed generalized multiscale finite element methods and applications},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Chak Shing Lee},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175800419920993},
  booktitle={Multiscale Modeling & Simulation},
  volume={13},
  number={1},
  pages={338-366},
  year={2015},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Chak Shing Lee. Mixed generalized multiscale finite element methods and applications. 2015. Vol. 13. In Multiscale Modeling & Simulation. pp.338-366. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175800419920993.
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