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Sármány, D. and Botchev, M.A. and van der Vegt, J.J.W. and Verwer, J.G. (2009) Comparing DG and Nedelec finite element discretisations of the second-order time-domain Maxwell equation. Memorandum 1912, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850
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This article compares the discontinuous Galerkin finite element method (DG-FEM) with the -conforming FEM in the discretisation of the second-order time-domain Maxwell equations with possibly nonzero conductivity term. While DG-FEM suffers from an increased number of degrees of freedom compared with -conforming FEM, it has the advantage of a purely block-diagonal mass matrix. This means that, as long as an explicit time-integration scheme is used, it is no longer necessary to solve a linear system at each time step -- a clear advantage over -conforming FEM. It is known that DG-FEM generally favours high-order methods whereas -conforming FEM is more suitable for low-order ones. The novelty we provide in this work is a direct comparison of the performance of the two methods when hierarchic -conforming basis functions are used up to polynomial order . The motivation behind this choice of basis functions is its growing importance in the development of - and -adaptive FEMs.
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