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 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1227-1257 |
| Journal | Multiscale Modeling and Simulation |
| Volume | 16 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2018 |
| Externally published | Yes |
Bibliographical 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 [email protected].Research Keywords
- Adaptivity
- Discontinuous Galerkin method
- High-contrast flow
- Model reduction
- Multiscale finite element method