High-order continuous and discontinuous Galerkin methods for wave problems

Authors

  • Giorgio Giorgiani,

    1. Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya–BarcelonaTech, Jordi Girona 1, 08034 Barcelona, Spain
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  • David Modesto,

    1. Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya–BarcelonaTech, Jordi Girona 1, 08034 Barcelona, Spain
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  • Sonia Fernández-Méndez,

    1. Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya–BarcelonaTech, Jordi Girona 1, 08034 Barcelona, Spain
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  • Antonio Huerta

    Corresponding author
    1. Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya–BarcelonaTech, Jordi Girona 1, 08034 Barcelona, Spain
    • Correspondence to: Antonio Huerta, Laboratori de Càlcul Numèric (LaCàN), E.T.S. Ingenieros de Caminos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain.

      E-mail: antonio.huerta@upc.es

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SUMMARY

Three Galerkin methods—continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin—are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin. Copyright © 2013 John Wiley & Sons, Ltd.

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