Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation
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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.
KeywordsDiscontinuous Galerkin method Energy conserving Dispersion analysis
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