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

Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 727-753.

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.

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