Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case
Paul Houston1, Ilaria Perugia2, Anna Schneebeli3 and Dominik Schötzau4
Department of Mathematics,
University of Leicester,
Leicester LE1 7RH, England. Paul.Houston@mcs.le.ac.uk
2 Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. email@example.com
3 Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland. firstname.lastname@example.org
4 Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver V6T 1Z2, Canada. email@example.com
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.
Mathematics Subject Classification: 65N30
Key words: Discontinuous Galerkin methods / mixed methods / time-harmonic Maxwell's equations.
© EDP Sciences, SMAI, 2005