On the approximation of Maxwell's eigenproblem in general 2D domains

In this paper we review some finite element methods to approximate the eige nvalues of Maxwell equations. The numerical schemes we are going to conside r are based on two different Variational formulations. Our aim is to compar e 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 pena lized 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 eleme nts are efficient. Moreover we propose a new nonstandard finite element met hod in order to deal with the penalized formulation in presence of reentran t corners: a biquadratic element with a suitable projection. (C) 2001 Elsev ier Science Ltd. All rights reserved.