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Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems

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

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Authors

Andrea Cangiani

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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