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

Paul Houston; Ilaria Perugia; Anna Schneebeli; Dominik Schötzau

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

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topHouston, Paul, et al. "Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.4 (2005): 727-753. <http://eudml.org/doc/245957>.

@article{Houston2005,

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 $L^2$-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 - Modélisation Mathématique et Analyse Numérique},

keywords = {discontinuous Galerkin methods; mixed methods; time-harmonic Maxwell’s equations; time-harmonic Maxwell's equations; interior penalty method},

language = {eng},

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/245957},

volume = {39},

year = {2005},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2005

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 $L^2$-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; time-harmonic Maxwell's equations; interior penalty method

UR - http://eudml.org/doc/245957

ER -

## References

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