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Goal-Oriented Error Analysis of a DG Scheme for a Second Gradient Elastodynamics Model

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Book cover Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects (FVCA 2017)

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Abstract

In this note we propose a discontinuous Galerkin in space, continuous Galerkin in time method for a problem arising in elastodynamics with phase transition. We make use of a dispersion operator from (Bona et al., Math. Comput. 82(283), 1401–1432, 2013) [3] allowing us to construct a consistent scheme. We derive goal-oriented a posteriori error estimators for this scheme based on dual weighted residuals. We conclude by summarising extensive numerical experiments.

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Acknowledgements

T.P. gratefully acknowledges support of the EPSRC grant EP/P000835/1. J.G. gratefully acknowledges support of the Baden-Württemberg fundation for the project “Numerical Methods for Multi-Phase Flows with Strongly Varying Mach Numbers”.

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Authors and Affiliations

  1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Jan Giesselmann

  2. Department of Mathematics and Statistics, University of Reading, Whiteknights, PO Box 220, Reading, GB-RG6 6AX, England

    Tristan Pryer

Authors
  1. Jan Giesselmann
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  2. Tristan Pryer
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Correspondence to Jan Giesselmann .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Giesselmann, J., Pryer, T. (2017). Goal-Oriented Error Analysis of a DG Scheme for a Second Gradient Elastodynamics Model. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_39

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