Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell’s equations on Cartesian grids

Eric T. Chung 1 Patrick Ciarlet 2 Tang Fei Yu 1
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell's equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee's scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. Numerical results are shown to confirm our theoretical statements, and applications to problems in unbounded domains with the use of PML are presented. A comparison of our staggered method and non-staggered method is carried out and shows that our method has better accuracy and efficiency.
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https://hal.inria.fr/hal-00937679
Contributeur : Valentin Vinoles <>
Soumis le : mardi 28 janvier 2014 - 17:06:14
Dernière modification le : jeudi 9 février 2017 - 15:50:25

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Eric T. Chung, Patrick Ciarlet, Tang Fei Yu. Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell’s equations on Cartesian grids. Journal of Computational Physics, Elsevier, 2013, 235, pp.14--31. <10.1016/j.jcp.2012.10.019>. <hal-00937679>

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