An Adaptive Generalized Multiscale Discontinuous Galerkin Method for High-Contrast Flow Problems
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AbstractIn 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, SIAM Rev., 43 (2001), pp. 129--159]). The proposed error indicators are $L_2$-based and can be inexpensively computed, which makes our approach efficient. Numerical results are presented that demonstrate the robustness of the proposed error indicators.
All Author(s) ListEric Chung, Yalchin Efendiev, Wing Tat Leung
Journal nameMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Year2018
Month8
Volume Number16
Issue Number3
Pages1227 - 1257
ISSN1540-3459
eISSN1540-3467
LanguagesEnglish-United States

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