Finite element approximation of Maxwell eigenproblems on curved Lipschitz polyhedral domains

Abstract

This paper deals with the finite element approximation of the spectral problem for the Maxwell equation on a curved non-convex Lipschitz polyhedral domain Ω. Convergence and optimal order error estimates are proved for the lowest order edge finite element space of Nédélec on a tetrahedral mesh of approximate domains Ω h ⊄ Ω . These convergence results are based on the discrete compactness property which is proved to hold true also in this case.