An Adaptive Generalized Multiscale Discontinuous Galerkin Method for High-Contrast Flow Problems

Eric T. Chung, Yalchin R. Efendiev, Wing Tat Leung

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

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, SIAM Rev., 43 (2001), pp. 129-159]). The proposed error indicators are L-based and can be inexpensively computed, which makes our approach efficient. Numerical results are presented that demonstrate the robustness of the proposed error indicators.
Original languageEnglish (US)
Pages (from-to)1227-1257
Number of pages31
JournalMultiscale Modeling & Simulation
Volume16
Issue number3
DOIs
StatePublished - Aug 7 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The first author was partially supported by the Hong Kong RGC General Research Fund (project 400813) and CUHK Direct Grant for Research 2013/14.

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