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

Paul Houston; Ilaria Perugia; Anna Schneebeli; Dominik Schötzau

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 4, page 727-753
  • ISSN: 0764-583X

Abstract

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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 L2-norm. The theoretical results are confirmed in a series of numerical experiments.

How to cite

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Houston, Paul, et al. "Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case." ESAIM: Mathematical Modelling and Numerical Analysis 39.4 (2010): 727-753. <http://eudml.org/doc/194284>.

@article{Houston2010,
abstract = { 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. },
author = {Houston, Paul, Perugia, Ilaria, Schneebeli, Anna, Schötzau, Dominik},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Discontinuous Galerkin methods; mixed methods; time-harmonic Maxwell's equations.; discontinuous Galerkin methods; time-harmonic Maxwell's equations; interior penalty method},
language = {eng},
month = {3},
number = {4},
pages = {727-753},
publisher = {EDP Sciences},
title = {Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case},
url = {http://eudml.org/doc/194284},
volume = {39},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 4
SP - 727
EP - 753
AB - 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.
LA - eng
KW - Discontinuous Galerkin methods; mixed methods; time-harmonic Maxwell's equations.; discontinuous Galerkin methods; time-harmonic Maxwell's equations; interior penalty method
UR - http://eudml.org/doc/194284
ER -

References

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