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Sármány, D. and Botchev, M.A. and van der Vegt, J.J.W. (2012) Time-integration methods for finite element discretisations of the second-order Maxwell equation. Memorandum 1975, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850
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Official URL: http://www.math.utwente.nl/publications
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the -conforming FEM. For the spatial discretisation, hierarchic -conforming basis functions are used up to polynomial order over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.
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