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Efficiency of high-order elements for continuous and discontinuous Galerkin methods

Authors

  • 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, 08034 Barcelona, Spain
    2. Civil & Computational Engineering Centre, College of Engineering, Swansea University, Swansea, UK
    • Correspondence to: Antonio Huerta, Laboratori de Càlcul Numèric (LaCàN), Departament de Matematica Aplicada III E.T.S. Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain.

      E-mail: antonio.huerta@upc.edu

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  • Aleksandar Angeloski,

    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, 08034 Barcelona, Spain
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  • Xevi Roca,

    1. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA
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  • Jaime Peraire

    1. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA
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SUMMARY

To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high-order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two-dimensional and three-dimensional domains for simplices and parallelotopes. Moreover, both element-wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high-order methods are more efficient than linear ones. Copyright © 2013 John Wiley & Sons, Ltd.

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