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 -norm. The theoretical results are confirmed in a series of numerical experiments.
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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {727--753},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {4},
doi = {10.1051/m2an:2005032},
mrnumber = {2165677},
zbl = {1087.65106},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2005032/}
}
TY - JOUR AU - Houston, Paul AU - Perugia, Ilaria AU - Schneebeli, Anna AU - Schötzau, Dominik TI - Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 727 EP - 753 VL - 39 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2005032/ DO - 10.1051/m2an:2005032 LA - en ID - M2AN_2005__39_4_727_0 ER -
%0 Journal Article %A Houston, Paul %A Perugia, Ilaria %A Schneebeli, Anna %A Schötzau, Dominik %T Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 727-753 %V 39 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2005032/ %R 10.1051/m2an:2005032 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 727-753. doi: 10.1051/m2an:2005032
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