Adaptive generalized multiscale finite element methods for H(curl)-elliptic problems with heterogeneous coefficients
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AbstractIn 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 offline-online 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.
All Author(s) ListEric T. Chung, Yanbo Li
Journal nameJournal of Computational and Applied Mathematics
Year2019
Month1
Day1
Volume Number345
PublisherELSEVIER
Pages357 - 373
ISSN0377-0427
eISSN1879-1778
LanguagesEnglish-United States

Last updated on 2020-21-10 at 02:55