High order edge finite element approximations for the time-harmonic Maxwell's equations

Abstract

The time-harmonic Maxwell's equations model the propagation of electromagnetic waves and are therefore fundamental equations for the simulation of many modern devices in everyday life. The numerical solution of these equations is hampered by some fundamental problems especially in the high frequency regime. Fine meshes have to be used in order to accurately represent the solution and also to avoid the pollution effect, which is very well known for the Helmholtz equations. We propose in this paper to address this problem by considering high order finite element approximations and in particular Whitney edge elements.