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Mixed discontinuous Galerkin approximationof the Maxwell operator: The indefinite case

Published online by Cambridge University Press:  15 August 2005

Paul Houston ,
Ilaria Perugia ,
Anna Schneebeli  and
Dominik Schötzau
Paul Houston
Affiliation:
Department of Mathematics, University of Leicester, Leicester LE1 7RH, England. Paul.Houston@mcs.le.ac.uk
Ilaria Perugia
Affiliation:
Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. ilaria.perugia@unipv.it
Anna Schneebeli
Affiliation:
Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland. anna.schneebeli@unibas.ch
Dominik Schötzau
Affiliation:
Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver V6T 1Z2, Canada. schoetzau@math.ubc.ca

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Abstract

We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp.22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg.191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal a priori error estimates in the energy-norm as well as the L2-norm. The theoretical results are confirmed in a series of numerical experiments.

Keywords

Discontinuous Galerkin methodsmixed methodstime-harmonic Maxwell's equations.

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 4 , July 2005 , pp. 727 - 753
Copyright
© EDP Sciences, SMAI, 2005

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