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Adaptive generalized multiscale finite element methods for H (curl)-elliptic problems with heterogeneous coefficients

Tsz Shun Eric CHUNG Yanbo Li

Numerical Analysis and Scientific Computing mathscidoc:1910.43573

Journal of Computational and Applied Mathematics, 345, 357-373, 2019.1
In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable snapshot space, and a dimensional reduction procedure to identify important modes of the solution. We next develop and analyze an a posteriori error indicator, and the corresponding adaptive algorithm. In addition, we will construct a coupled offlineonline adaptive algorithm, which provides an adaptive strategy to the selection of offline and online basis functions. Our theory shows that the convergence is robust with respect to the heterogeneities and contrast of the media. We present several numerical results to illustrate the performance of our method.
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@inproceedings{tsz2019adaptive,
  title={Adaptive generalized multiscale finite element methods for H (curl)-elliptic problems with heterogeneous coefficients},
  author={Tsz Shun Eric CHUNG, and Yanbo Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202714051113102},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={345},
  pages={357-373},
  year={2019},
}
Tsz Shun Eric CHUNG, and Yanbo Li. Adaptive generalized multiscale finite element methods for H (curl)-elliptic problems with heterogeneous coefficients. 2019. Vol. 345. In Journal of Computational and Applied Mathematics. pp.357-373. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202714051113102.
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