hp-Version Discontinuous Galerkin Approximations of the Elastodynamics Equation
In this paper we extend the results contained in Antonietti et al. (J Sci Comput 68(1):143-170, 2016) and consider the problem of approximating the elastodynamics equation by means of hp-version discontinuous Galerkin methods. For the resulting semi-discretized schemes we derive stability bounds as well as hp error estimates in the energy and L 2-norms. Our theoretical estimates are verified through three dimensional numerical experiments.
Paola F. Antonietti and Ilario Mazzieri have been partially supported by the research grant no. 2015-0182 funded by Fondazione Cariplo and Regione Lombardia. Part of this work has been completed while Paola F. Antonietti was visiting the Institut Henri Poincaré (IHP), Paris. She thanks the Institute for the kind hospitality.
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