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High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation

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Abstract

In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibility of simplicial elements and the computational efficiency of dG methods. We analyze the dissipation, dispersion and stability properties of the resulting scheme, with a focus on the choice of different sets of basis functions. Finally, we apply the method on benchmark as well as realistic test cases.

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Authors and Affiliations

  1. MOX-Laboratory for Modeling and Scientific Computing, Department of Mathematics, Politecnico di Milano, P.za Leonardo da Vinci, 32, 20133, Milano, Italy

    Paola F. Antonietti & Ilario Mazzieri

  2. Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, F-75005, Paris, France

    Carlo Marcati

  3. CMCS, École Polytechnique Fédérale de Lausanne (EPFL), Station 8, 1015, Lausanne, Switzerland

    Alfio Quarteroni

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  1. Paola F. Antonietti
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  2. Carlo Marcati
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  3. Ilario Mazzieri
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  4. Alfio Quarteroni
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Correspondence to Ilario Mazzieri.

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Antonietti, P.F., Marcati, C., Mazzieri, I. et al. High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation. Numer Algor 71, 181–206 (2016). https://doi.org/10.1007/s11075-015-0021-7

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  • DOI: https://doi.org/10.1007/s11075-015-0021-7

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