An adaptive generalized multiscale discontinuous galerkin method for high-contrast flow problems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

22 Scopus Citations
View graph of relations



Original languageEnglish
Pages (from-to)1227-1257
Journal / PublicationMultiscale Modeling and Simulation
Issue number3
Publication statusPublished - 2018
Externally publishedYes


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 L2-based and can be inexpensively computed, which makes our approach efficient. Numerical results are presented that demonstrate the robustness of the proposed error indicators.

Research Area(s)

  • Adaptivity, Discontinuous Galerkin method, High-contrast flow, Model reduction, Multiscale finite element method

Bibliographic Note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to