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
2 LIMSI, UPR 3251 CNRS, BP 133, 91403 Orsay cedex, France.
Revised: 10 June 2015
Accepted: 2 November 2016
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
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