Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations

D. Sarmany, Mikhail A. Bochev, Jacobus J.W. van der Vegt

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    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.
    Original languageUndefined
    Pages (from-to)47-74
    Number of pages35
    JournalJournal of scientific computing
    Issue numberLNCS4549/1
    Publication statusPublished - Jul 2007


    • Maxwell equations
    • High-order nodal discontinuous Galerkin methods · Maxwell equations · Numerical dispersion and dissipation · Strong-stability-preserving Runge-Kutta methods
    • EWI-10903
    • high-order nodal discontinuous Galerkin methods
    • numerical dispersion and dissipation strong-stability-preserving Runge-Kutta methods
    • MSC-65L06
    • MSC-65M20
    • MSC-65M60
    • METIS-241848
    • IR-64298

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