ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case

Houston, Paula1, Perugia, Ilariaa2, Schneebeli, Annaa3 and Schötzau, Dominika4

a1 Department of Mathematics, University of Leicester, Leicester LE1 7RH, England. Paul.Houston@mcs.le.ac.uk

a2 Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. ilaria.perugia@unipv.it

a3 Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland. anna.schneebeli@unibas.ch

a4 Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver V6T 1Z2, Canada. schoetzau@math.ubc.ca


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 L 2-norm. The theoretical results are confirmed in a series of numerical experiments.

(Received May 14 2004)

(Online publication August 15 2005)

Key Words:

  • Discontinuous Galerkin methods;
  • mixed methods;
  • time-harmonic Maxwell's equations.

Mathematics Subject Classification:

  • 65N30
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