Dispersion and Dissipation Error in High-Order Runge-Kutta Discontinuous Galerkin Discretisations of the Maxwell Equations

  • Authors:

  • D. Sármány;M. A. Botchev;J. J. Vegt

  • Affiliations:

  • Department of Applied Mathematics, University of Twente, AE Enschede, Netherlands 7500;Department of Applied Mathematics, University of Twente, AE Enschede, Netherlands 7500;Department of Applied Mathematics, University of Twente, AE Enschede, Netherlands 7500

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2007

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Abstract

Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared with fixed-order schemes. Moreover, this comes without a significant increase in the computational work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the fully discrete scheme. The analysis is carried out on both the one-dimensional and the two-dimensional fully discrete schemes and, in the latter case, on uniform as well as on non-uniform meshes. It also provides practical information on the convergence of the dissipation and dispersion error up to polynomial order 10 for the one-dimensional fully discrete scheme.