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.

a2 Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy.

a3 Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland.

a4 Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver V6T 1Z2, Canada.


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