Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems

Cangiani, Andrea; Georgoulis, Emmanuil H.; Metcalfe, Stephen

Abstract

© 2013 The authors. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin (dG) method discretization of a linear nonstationary convection-diffusion initial/boundary value problem and with the implementation of a corresponding adaptive algorithm. More specifically, we derive a posteriori bounds for the error in the L 2 (H 1) + L for an interior penalty dG discretization in space and a backward Euler discretization in time. Finally, an adaptive algorithm is proposed utilizing the error estimator. Optimal rate of convergence of the adaptive algorithm is observed in a number of test problems and for various Pèclet numbers.

Citation

Cangiani, A., Georgoulis, E. H., & Metcalfe, S. (2014). Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems. IMA Journal of Numerical Analysis, 34(4), 1578-1597. https://doi.org/10.1093/imanum/drt052

• Journal Article Type: Article
• Acceptance Date: Aug 22, 2012
• Online Publication Date: Oct 30, 2013
• Publication Date: Oct 1, 2014
• Deposit Date: Aug 9, 2019
• Journal: IMA Journal of Numerical Analysis
• Print ISSN: 0272-4979
• Electronic ISSN: 1464-3642
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 4
• Pages: 1578-1597
• DOI: https://doi.org/10.1093/imanum/drt052
• Public URL: https://nottingham-repository.worktribe.com/output/2411271
• Publisher URL: https://academic.oup.com/imajna/article/34/4/1578/880229