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Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error Analysis

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Abstract

We present an arbitrary high-order local discontinuous Galerkin (LDG) method with alternating fluxes for solving linear elastodynamics problems in isotropic media. Both the semi-discrete analysis and fully discrete analysis for a leap-frog LDG method are given to show that the proposed method simultaneously enjoys the energy conserving property and optimal convergence rates in both the displacement and stress, when the tensor product polynomials of the degree k are used on Cartesian meshes. Numerical experiments demonstrate that the proposed method has several advantages including the exact energy conservation, slow-growing errors in long time simulation, and subtle dependence on the first Lamé parameter \(\lambda \).

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA

    Ruchi Guo

  2. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Yulong Xing

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  1. Ruchi Guo
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  2. Yulong Xing
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Y. Xing: The work of this author is partially supported by the NSF grant DMS-1753581.

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Guo, R., Xing, Y. Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error Analysis. J Sci Comput 87, 13 (2021). https://doi.org/10.1007/s10915-021-01418-x

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