Adaptive discontinuous Galerkin methods for elliptic interface problems

Cangiani, Andrea; Georgoulis, Emmanuil H.; Sabawi, Younis A.

Abstract

© 2017 American Mathematical Society. An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with fluxbalancing interface conditions, e.g., modelling mass transfer of solutes through semi-permeable membranes, is considered. The method allows for extremely general curved element shapes employed to resolve the interface geometry exactly. A residual-type a posteriori error estimator for this dG method is proposed and upper and lower bounds of the error in the respective dG-energy norm are proven. The a posteriori error bounds are subsequently used to prove a basic a priori convergence result. The theory presented is complemented by a series of numerical experiments. The presented approach applies immediately to the case of curved domains with non-essential boundary conditions, too.

Citation

Cangiani, A., Georgoulis, E. H., & Sabawi, Y. A. (2018). Adaptive discontinuous Galerkin methods for elliptic interface problems. Mathematics of Computation, 87(314), 2675-2707. https://doi.org/10.1090/mcom/3322

• Journal Article Type: Article
• Acceptance Date: May 31, 2017
• Online Publication Date: Feb 20, 2018
• Publication Date: Jan 1, 2018
• Deposit Date: Aug 9, 2019
• Journal: Mathematics of Computation
• Print ISSN: 0025-5718
• Electronic ISSN: 1088-6842
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 87
• Issue: 314
• Pages: 2675-2707
• DOI: https://doi.org/10.1090/mcom/3322
• Public URL: https://nottingham-repository.worktribe.com/output/2411179
• Publisher URL: https://www.ams.org/journals/mcom/2018-87-314/S0025-5718-2018-03322-1/