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J Sci Comput (2007) 33: 4774 DOI 10.1007/s10915-007-9143-y

Summary: J Sci Comput (2007) 33: 47­74
DOI 10.1007/s10915-007-9143-y
Dispersion and Dissipation Error in High-Order
Runge-Kutta Discontinuous Galerkin Discretisations
of the Maxwell Equations
D. Sármány · M.A. Botchev · J.J.W. van der Vegt
Received: 21 December 2006 / Accepted: 13 June 2007 / Published online: 14 July 2007
© Springer Science+Business Media, LLC 2007
Abstract Different time-stepping methods for a nodal high-order discontinuous Galerkin
discretisation of the Maxwell equations are discussed. A comparison between the most pop-
ular 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 dis-
cretisation, 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 dis-
crete 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


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering