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HP a-priori error estimates for a non-dissipative spectral discontinuous Galerkin method to solve the Maxwell equations in the time domain


Authors: S. Pernet and X. Ferrieres
Journal: Math. Comp. 76 (2007), 1801-1832
MSC (2000): Primary 35B45; Secondary 65M12
Published electronically: April 20, 2007
MathSciNet review: 2336269
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Abstract: In this paper, we present the $ hp$-convergence analysis of a non-dissipative high-order discontinuous Galerkin method on unstructured hexahedral meshes using a mass-lumping technique to solve the time-dependent Maxwell equations. In particular, we underline the spectral convergence of the method (in the sense that when the solutions and the data are very smooth, the discretization is of unlimited order). Moreover, we see that the choice of a non-standard approximate space (for a discontinuous formulation) with the absence of dissipation can imply a loss of spatial convergence. Finally we present a numerical result which seems to confirm this property.


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Additional Information

S. Pernet
Affiliation: CERFACS (European Centre for Research and Advanced Training in Scientific Computation) 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France
Email: pernet@cerfacs.fr

X. Ferrieres
Affiliation: ONERA, 2 avenue Edouard Belin, 31055 Toulouse, France
Email: ferrieres@onecert.fr

DOI: https://doi.org/10.1090/S0025-5718-07-01991-6
Received by editor(s): June 20, 2005
Received by editor(s) in revised form: June 4, 2006
Published electronically: April 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.