Andrea Cangiani
Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems
Cangiani, Andrea; Georgoulis, Emmanuil H; Sabawi, Younis
Authors
Emmanuil H Georgoulis
Younis Sabawi
Abstract
We prove a basic error contraction result of an adaptive discontinuous Galerkin method for an elliptic interface problem. The interface conditions considered model mass transfer of solutes through semi-permeable membranes and other filtering processes. The adaptive algorithm is based on a residual-type a posteriori error estimator, with a bulk refinement criterion. The a posteriori error bound is derived under the assumption that the triangulation is aligned with the interfaces although, crucially, extremely general curved element shapes are also allowed, resolving the interface geometry exactly. As a corollary, convergence of the adaptive discontinuous Galerkin method for non-essential Neumann-and/or Robin-type boundary conditions, posed on general curved boundaries, also follows. Numerical experiments are also presented. Keywords: Discontinuous Galerkin method, interface problem, a posteriori error bound, adaptivity, convergence analysis, a posteriori error analysis on curved domains.
Citation
Cangiani, A., Georgoulis, E. H., & Sabawi, Y. (2020). Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems. Journal of Computational and Applied Mathematics, 367, Article 112397. https://doi.org/10.1016/j.cam.2019.112397
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 9, 2019 |
Online Publication Date | Aug 23, 2019 |
Publication Date | Mar 15, 2020 |
Deposit Date | Aug 14, 2019 |
Publicly Available Date | Mar 29, 2024 |
Journal | Journal of Computational and Applied Mathematics |
Print ISSN | 0377-0427 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 367 |
Article Number | 112397 |
DOI | https://doi.org/10.1016/j.cam.2019.112397 |
Keywords | Applied Mathematics; Computational Mathematics |
Public URL | https://nottingham-repository.worktribe.com/output/2428770 |
Publisher URL | https://www.sciencedirect.com/science/article/pii/S0377042719304005 |
Additional Information | This article is maintained by: Elsevier; Article Title: Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems; Journal Title: Journal of Computational and Applied Mathematics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.cam.2019.112397; Content Type: article; Copyright: © 2019 Elsevier B.V. All rights reserved. |
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