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The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations


Authors: Ilaria Perugia and Dominik Schötzau
Journal: Math. Comp. 72 (2003), 1179-1214
MSC (2000): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-02-01471-0
Published electronically: October 18, 2002
MathSciNet review: 1972732
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Abstract: The local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equations in a low-frequency regime is introduced and analyzed. Topologically nontrivial domains and heterogeneous media are considered, containing both conducting and insulating materials. The presented method involves discontinuous Galerkin discretizations of the curl-curl and grad-div operators, derived by introducing suitable auxiliary variables and so-called numerical fluxes. An $hp$-analysis is carried out and error estimates that are optimal in the meshsize $h$ and slightly suboptimal in the approximation degree $p$ are obtained.


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Additional Information

Ilaria Perugia
Affiliation: Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy
Email: perugia@dimat.unipv.it

Dominik Schötzau
Affiliation: Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
Email: schotzau@math.unibas.ch

DOI: https://doi.org/10.1090/S0025-5718-02-01471-0
Keywords: $hp$-finite elements, discontinuous Galerkin methods, low-frequency time-harmonic Maxwell equations, heterogeneous media
Received by editor(s): July 9, 2001
Received by editor(s) in revised form: December 10, 2001
Published electronically: October 18, 2002
Additional Notes: The first author was supported in part by NSF Grant DMS-9807491 and by the University of Minnesota Supercomputing Institute. This work was carried out when the author was visiting the School of Mathematics, University of Minnesota.
The second author was supported in part by NSF Grant DMS-0107609 and by the University of Minnesota Supercomputing Institute. This work was carried out while the author was affiliated with the School of Mathematics, University of Minnesota.
Article copyright: © Copyright 2002 American Mathematical Society

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