Volume 39, Number 4, July-August 2005
|Page(s)||727 - 753|
|Published online||15 August 2005|
Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case
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. firstname.lastname@example.org
3 Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland. email@example.com
4 Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver V6T 1Z2, Canada. firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.