An Interior Penalty Method with $C^0$ Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

摘要

The present paper proposes and analyzes an interior penalty technique using$C^0$-finite elements to solve the Maxwell equations in domains withheterogeneous properties. The convergence analysis for the boundary valueproblem and the eigenvalue problem is done assuming only minimal regularity inLipschitz domains. The method is shown to converge for any polynomial degreesand to be spectrally correct.