On the approximation of Maxwellʹs eigenproblem in general 2D domains

In this paper we review some finite element methods to approximate the eigenvalues of Maxwell equations. The numerical schemes we are going to consider are based on two different variational formulations. Our aim is to compare the performances of the methods depending on the shape of the domain. We shall see that the nodal elements can give good results only using the penalized formulation and only if the domain is a convex or smooth polygon. In the case of domains with reentrant corners it turns out that the edge elements are efficient. Moreover we propose a new non-standard finite element method in order to deal with the penalized formulation in presence of reentrant corners: a biquadratic element with a suitable projection.