Computational models of electromagnetic resonators: Analysis of edge element approximation

The purpose of this paper is to address some difficulties which arise in computing the eigenvalues of the Maxwell\u27s system by a finite element method. Depending on the used method, the spectrum may be polluted by spurious modes which are difficult to pick out among the approximations of the physically correct eigenvalues. Here we prove, under very general assumptions, that using edge elements the discrete spectrum well approximates the correct one and we give some justification of the spectral pollution which occurs when nodal elements are used. Results of numerical experiments confirming the theory are also reported