Geodesic
Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 4, pp. 727-753

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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 : 10.1051/m2an:2005032
Classification : 65N30
Keywords: discontinuous Galerkin methods, mixed methods, time-harmonic Maxwell's equations 
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     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 },
     pages = {727--753},
     publisher = {EDP-Sciences},
     volume = {39},
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     year = {2005},
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     zbl = {1087.65106},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005032/}
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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 , Tome 39 (2005) no. 4, pp. 727-753. doi: 10.1051/m2an:2005032

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