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Residual-driven online generalized multiscale finite element methods

Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung

Numerical Analysis and Scientific Computing mathscidoc:1910.43466

Journal of Computational Physics, 302, 176-190, 2015.12
The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are constructed using Generalized Multiscale Finite Element Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee that additional online multiscale basis functions will reduce
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@inproceedings{tsz2015residual-driven,
  title={Residual-driven online generalized multiscale finite element methods},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175830938559995},
  booktitle={Journal of Computational Physics},
  volume={302},
  pages={176-190},
  year={2015},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung. Residual-driven online generalized multiscale finite element methods. 2015. Vol. 302. In Journal of Computational Physics. pp.176-190. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175830938559995.
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