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Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation

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Abstract

The dispersive behavior of the recently proposed energy-conserving discontinuous Galerkin (DG) method by Fu and Shu (Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems, 2018. arXiv:1804.10307) is analyzed and compared with the classical centered and upwinding DG schemes. It is shown that the new scheme gives a significant improvement over the classical centered and upwinding DG schemes in terms of dispersion error. Numerical results are presented to support the theoretical findings.

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References

  1. Abgrall, R., Shu, C.-W. (eds.): Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues. Handbook of Numerical Analysis, vol. 17. Elsevier, Amsterdam (2016)

    MATH  Google Scholar 

  2. Abgrall, R., Shu, C.-W. (eds.): Handbook of Numerical Methods for Hyperbolic Problems: Applied and Modern Issues. Handbook of Numerical Analysis, vol. 18. Elsevier, Amsterdam (2017)

    MATH  Google Scholar 

  3. Ainsworth, M.: Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. J. Comput. Phys. 198, 106–130 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ainsworth, M.: Dispersive behaviour of high order finite element schemes for the one-way wave equation. J. Comput. Phys. 259, 1–10 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ainsworth, M., Monk, P., Muniz, W.: Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. J. Sci. Comput. 27, 5–40 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cockburn, B., Karniadakis, G.E., Shu, C.-W.: The development of discontinuous Galerkin methods. In: Discontinuous Galerkin methods (Newport, RI, 1999), vol. 11. Lecture Notes Computational Science and Engineering. Springer, Berlin, pp. 3–50 (2000)

  7. Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35, 2440–2463 (1998). (electronic)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cohen, G.C.: Higher-Order Numerical Methods for Transient Wave Equations. Scientific Computation. Springer, Berlin (2002)

    Book  Google Scholar 

  9. Durran, D.R.: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Texts in Applied Mathematics, vol. 32. Springer, New York (1999)

    Book  Google Scholar 

  10. Fu, G., Shu, C.-W.: Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems, arXiv:1804.10307 [math.NA] (2018)

  11. Ihlenburg, F.: Finite Element Analysis of Acoustic Scattering. Applied Mathematical Sciences, vol. 132. Springer, New York (1998)

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George St, Providence, RI, 02912, USA

    Mark Ainsworth & Guosheng Fu

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  1. Mark Ainsworth
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  2. Guosheng Fu
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Correspondence to Guosheng Fu.

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Ainsworth, M., Fu, G. Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation. J Sci Comput 79, 209–226 (2019). https://doi.org/10.1007/s10915-018-0846-z

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  • DOI: https://doi.org/10.1007/s10915-018-0846-z

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