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Adaptive discontinuous Galerkin methods for elliptic interface problems

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journal contribution
posted on 12.03.2018, 09:48 by Andrea Cangiani, Emmanuil H. Georgoulis, Younis A. Sabawi
An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with flux-balancing 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.

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Citation

Mathematics of Computation, 2018, 87, pp. 2675-2707

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Mathematics of Computation

Publisher

American Mathematical Society

issn

0025-5718

eissn

1088-6842

Acceptance date

01/09/2017

Copyright date

2018

Available date

12/03/2018

Publisher version

http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2018-03322-1/

Language

en

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