| Issue |
ESAIM: M2AN
Volume 39, Number 4, July-August 2005
|
|
|---|---|---|
| Page(s) | 727 - 753 | |
| DOI | https://doi.org/10.1051/m2an:2005032 | |
| Published online | 15 August 2005 | |
Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case
1
Department of Mathematics,
University of Leicester,
Leicester LE1 7RH, England. Paul.Houston@mcs.le.ac.uk
2
Dipartimento di Matematica,
Università di Pavia,
Via Ferrata 1, 27100 Pavia, Italy.
ilaria.perugia@unipv.it
3
Department of Mathematics,
University of Basel,
Rheinsprung 21, 4051 Basel, Switzerland.
anna.schneebeli@unibas.ch
4
Mathematics Department, University of British Columbia,
121-1984 Mathematics Road, Vancouver V6T 1Z2, Canada.
schoetzau@math.ubc.ca
Received:
14
May
2004
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.
Mathematics Subject Classification: 65N30
Key words: Discontinuous Galerkin methods / mixed methods / time-harmonic Maxwell's equations.
© EDP Sciences, SMAI, 2005
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