| Issue |
ESAIM: M2AN
Volume 50, Number 5, September-October 2016
|
|
|---|---|---|
| Page(s) | 1457 - 1489 | |
| DOI | https://doi.org/10.1051/m2an/2015086 | |
| Published online | 08 September 2016 | |
An Interior Penalty Method with C0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity∗
1 Department of Mathematics, Texas
A&M University, College
Station, TX
77843-3368,
USA.
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2 LIMSI, UPR 3251 CNRS,
BP 133, 91403
Orsay cedex,
France.
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Received:
16
September
2014
Revised:
10
June
2015
Accepted:
2
November
2016
Abstract
The present paper proposes and analyzes an interior penalty technique using C0-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally correct.
Mathematics Subject Classification: 65N25 / 65F15 / 35Q60
Key words: Finite elements / Maxwell equations / eigenvalue / discontinuous coefficients / spectral approximation
This material is based upon work supported in part by the National Science Foundation grants DMS-1254618, DMS-1015984. Parts of this work was done during visits of Francky Luddens at Texas A&M. The support of the University Paris-Sud 11 is acknowledged.
© EDP Sciences, SMAI 2016
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