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A stabilized cut discontinuous Galerkin framework for elliptic boundary value and interface problems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Mathematical Sciences, Norwegian University of Science and Technology, NO 7491, Trondheim, Norway.
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 348, p. 466-499Article in journal (Refereed) Published
Abstract [en]

We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of elliptic boundary value and interface problems on complicated domains. The domain of interest is embedded in a structured, unfitted background mesh in R d , so that the boundary or interface can cut through it in an arbitrary fashion. The method is based on an unfitted variant of the classical symmetric interior penalty method using piecewise discontinuous polynomials defined on the background mesh. Instead of the cell agglomeration technique commonly used in previously introduced unfitted discontinuous Galerkin methods, we employ and extend ghost penalty techniques from recently developed continuous cut finite element methods, which allows for a minimal extension of existing fitted discontinuous Galerkin software to handle unfitted geometries. Identifying four abstract assumptions on the ghost penalty, we derive geometrically robust a priori error and condition number estimates for the Poisson boundary value problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. We also demonstrate how the framework can be elegantly applied to discretize high contrast interface problems. The theoretical results are illustrated by a number of numerical experiments for various approximation orders and for two and three-dimensional test problems. (C) 2018 Published by Elsevier B.V.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 348, p. 466-499
Keywords [en]
Elliptic problems, Discontinuous Galerkin, Cut finite element method, Stabilization, Condition number, A priori error estimates
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-158064DOI: 10.1016/j.cma.2018.12.041ISI: 000462472400019OAI: oai:DiVA.org:umu-158064DiVA, id: diva2:1305016
Funder
The Kempe Foundations, JCK-1612Swedish Research Council, 2017-05038Available from: 2019-04-15 Created: 2019-04-15 Last updated: 2019-04-15Bibliographically approved

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Gürkan, CerenMassing, André

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