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An adaptive generalized multiscale discontinuous Galerkin method for high-contrast flow problems

Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung

Numerical Analysis and Scientific Computing mathscidoc:1910.43525

Multiscale Modeling & Simulation, 16, (3), 1227-1257, 2014.8
In this paper, we develop an adaptive generalized multiscale discontinuous Galerkin method (GMsDGM) for a class of high-contrast flow problems and derive a priori and a posteriori error estimates for the method. Based on the a posteriori error estimator, we develop an adaptive enrichment algorithm for our GMsDGM and prove its convergence. The adaptive enrichment algorithm gives an automatic way to enrich the approximation space in regions where the solution requires more basis functions, which are shown to perform well compared with a uniform enrichment. We also discuss an approach that adaptively selects multiscale basis functions by correlating the residual to multiscale basis functions (cf. [S. S. Chen, D. L. Donoho, and M. A. Saunders, <i>SIAM Rev.</i>, 43 (2001), pp. 129--159]). The proposed error indicators are L_2-based and can be inexpensively computed, which makes our approach efficient
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@inproceedings{tsz2014an,
  title={An adaptive generalized multiscale discontinuous Galerkin method for high-contrast flow problems},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181924143226054},
  booktitle={Multiscale Modeling &amp; Simulation},
  volume={16},
  number={3},
  pages={1227-1257},
  year={2014},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung. An adaptive generalized multiscale discontinuous Galerkin method for high-contrast flow problems. 2014. Vol. 16. In Multiscale Modeling &amp; Simulation. pp.1227-1257. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181924143226054.
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