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Journal of Scientific Computing

Erschienen in:

28.01.2017

eXtended Hybridizable Discontinuous Galerkin with Heaviside Enrichment for Heat Bimaterial Problems

verfasst von: Ceren Gürkan, Martin Kronbichler, Sonia Fernández-Méndez

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2017

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Abstract

A novel strategy for the hybridizable discontinuous Galerkin (HDG) solution of heat bimaterial problems is proposed. It is based on eXtended finite element philosophy, together with a level set description of interfaces. Heaviside enrichment on cut elements and cut faces is used to represent discontinuities across the interface. A suitable weak form for the HDG local problem on cut elements is derived, accounting for the discontinuous enriched approximation, and weakly imposing continuity or jump conditions over the material interface. The computational mesh is not required to fit the interface, simplifying and reducing the cost of mesh generation and, in particular, avoiding continuous remeshing for evolving interfaces. Numerical experiments demonstrate that X-HDG keeps the accuracy of standard HDG methods in terms of optimal convergence and superconvergence.

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Titel: eXtended Hybridizable Discontinuous Galerkin with Heaviside Enrichment for Heat Bimaterial Problems
verfasst von: Ceren Gürkan
Martin Kronbichler
Sonia Fernández-Méndez
Publikationsdatum: 28.01.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0370-6

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