Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation

TL;DR

This paper analyzes the dispersive properties of a new energy-conserving discontinuous Galerkin method for the one-way wave equation, demonstrating its superior dispersion error performance over classical schemes through theoretical and numerical comparisons.

Contribution

It introduces and evaluates an energy-conserving DG scheme, showing significant improvements in dispersion error over classical methods.

Findings

The new scheme reduces dispersion error compared to classical schemes.

Numerical results confirm theoretical dispersion error improvements.

Energy conservation is maintained in the proposed DG method.

Abstract

The dispersive behavior of the recently proposed energy-conserving discontinuous Galerkin (DG) method by Fu and Shu [10] 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.