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

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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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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Keywords

  • Discontinuous Galerkin method
  • Energy conserving
  • Dispersion analysis