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eXtended Hybridizable Discontinuous Galerkin with Heaviside Enrichment for Heat Bimaterial Problems

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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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Acknowledgements

This work was supported by the DAFOH2 Project (Ministerio de Economia y Competitividad, MTM2013-46313-R), the Erasmus Mundus Joint Doctorate SEED Project (European Comission, 2013-1436/001-001-EMJD) and the Catalan Goverment (Generalitat de Catalunya, 2009SGR875). The authors also acknowledge Ms. Esther Sala-Lardies (Universitat Politècnica de Catalunya) for letting them use her library for numerical integration in cut elements, and Prof. John E. Dolbow (Duke University) for the interesting discussions they had on the competitiveness of X-HDG in front of standard X-FEM.

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Authors and Affiliations

  1. Laboratori de Càlcul Numèric (LaCàN), Universitat Politècnica de Catalunya (UPC), Barcelona, Spain

    Ceren Gürkan & Sonia Fernández-Méndez

  2. Institute for Computational Mechanics, Technical University of Munich, Garching, Germany

    Martin Kronbichler

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  1. Ceren Gürkan
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  2. Martin Kronbichler
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  3. Sonia Fernández-Méndez
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Correspondence to Sonia Fernández-Méndez.

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Gürkan, C., Kronbichler, M. & Fernández-Méndez, S. eXtended Hybridizable Discontinuous Galerkin with Heaviside Enrichment for Heat Bimaterial Problems. J Sci Comput 72, 542–567 (2017). https://doi.org/10.1007/s10915-017-0370-6

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  • DOI: https://doi.org/10.1007/s10915-017-0370-6

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