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10903 Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations
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Sármány, D. and Botchev, M.A. and van der Vegt, J.J.W. (2007) Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations. Journal of scientific computing, 33 (1). pp. 47-74. ISSN 0885-7474 *** ISI Impact 1,946 ***

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Official URL: http://dx.doi.org/10.1007/s10915-007-9143-y

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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.

Item Type:Article
Research Group:EWI-MACS: Mathematics of Computational Science
Research Program:IMPACT-Mechanics of Fluids and Solids, IMPACT-General, MESA-General
Research Project:BRICKS/MSV1.5: Hp-Adaptive Finite Element Methods for the Maxwell Equations, BRICKS/MSV1: Scientific computing
Additional Information:Please note different possible spellings of second author's name: "Botchev" or "Bochev".
Uncontrolled Keywords:high-order nodal discontinuous Galerkin methods, Maxwell equations, numerical dispersion and dissipation
strong-stability-preserving Runge-Kutta methods
ID Code:10903
Status:Published
Deposited On:21 January 2008
Refereed:Yes
International:Yes
ISI Impact Factor:1,946
More Information:statisticsmetis

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