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Journal of Scientific Computing

, Volume 72, Issue 2, pp 542–567 | Cite as

eXtended Hybridizable Discontinuous Galerkin with Heaviside Enrichment for Heat Bimaterial Problems

  • Ceren Gürkan
  • Martin Kronbichler
  • Sonia Fernández-MéndezEmail author
Article

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.

Keywords

Interface Bimaterial Hybridizable discontinuous Galerkin (HDG) High-order Level-sets X-FEM X-HDG 

Notes

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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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Laboratori de Càlcul Numèric (LaCàN)Universitat Politècnica de Catalunya (UPC)BarcelonaSpain
  2. 2.Institute for Computational MechanicsTechnical University of MunichGarchingGermany

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