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Dispersion Analysis of HDG Methods

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Abstract

This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for the wavenumber error for the lowest order Single Face HDG (SFH) method. The expansion shows that the SFH method exhibits convergence rates of the wavenumber errors comparable to that of the mixed hybrid Raviart–Thomas method. In addition, we observe the same behavior for the higher order cases in numerical experiments.

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Acknowledgements

This paper is the outgrowth of a suggestion from Prof. Bernardo Cockburn to go beyond the standard HDG method while comparing dispersion relations. On this occasion for celebrating Prof. Cockburn’s contributions, the authors would like to place on record their deep appreciation for his tireless efforts to nurture the mathematical community of researchers in discontinuous Galerkin methods over the years. This work was initiated while the student author F. Vargas was visiting Portland State University, thanks to the support from CONICYT, Chile. M. Solano was partially supported by Conicyt-Chile through Fondecyt project No. 1160320 and project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR, 97207-0751, USA

    Jay Gopalakrishnan

  2. Departamento de Ingeniería Matemática and Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción, Concepción, Chile

    Manuel Solano & Felipe Vargas

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  1. Jay Gopalakrishnan
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  2. Manuel Solano
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  3. Felipe Vargas
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Correspondence to Felipe Vargas.

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Gopalakrishnan, J., Solano, M. & Vargas, F. Dispersion Analysis of HDG Methods. J Sci Comput 77, 1703–1735 (2018). https://doi.org/10.1007/s10915-018-0781-z

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  • DOI: https://doi.org/10.1007/s10915-018-0781-z

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