Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, p. 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.

DOI : https://doi.org/10.1051/m2an:2005032
Classification:  65N30
Keywords: discontinuous Galerkin methods, mixed methods, time-harmonic Maxwell's equations
@article{M2AN_2005__39_4_727_0,
     author = {Houston, Paul and Perugia, Ilaria and Schneebeli, Anna and Sch\"otzau, Dominik},
     title = {Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     pages = {727-753},
     doi = {10.1051/m2an:2005032},
     zbl = {1087.65106},
     mrnumber = {2165677},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_4_727_0}
}
Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik. Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, pp. 727-753. doi : 10.1051/m2an:2005032. http://www.numdam.org/item/M2AN_2005__39_4_727_0/

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