An Interior Penalty Method with C0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

The present paper proposes and analyzes an interior penalty technique using C-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. Received September 16, 2014. Revised June 10, 2015. Accepted November 2, 2016.