Istituto di Matematica Applicata e Tecnologie Informatiche     
Boffi D., Farina M., Gastaldi L. On the approximation of Maxwell's eigenproblem in general 2D domains. Preprint ercim.cnr.ian//1999-1138, 1999.
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 two new non standard finite elements in order to deal with the penalized formulation in presence of reentrant corners: the nonconforming nodal elements and the biquadratic elements with projection.
Subject Fem, penalty method, nodal-edge elements, nonconforming elements, projection procedure
65N30, 65N25

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