Istituto di Matematica Applicata e Tecnologie Informatiche     
Boffi D., Gastaldi L. On the time harmonic Maxwell equations in general domains. Technical report ercim.cnr.ian//2001-1266, 2001.
In this paper we shall consider the finite element approximation to the Maxwell equations. We recall the convergence theory for the finite element approximation of the time harmonic Maxwell equations. The first analysis of this problem has been given by Monk under certain restrictions on the domain, on the coefficients and on the mesh sequence. Our analysis relies on the convergence of the discrete Maxwell eigenmodes towards the continuous ones. We study simple test cases in order to compare the accuracy of the edge element method to a penalized approach which makes use of standard nodal elements. Standard penalization with nodal elements is very efficient with smooth or convex domains (and regular coefficients), while it is known to produce very bad results in presence of singularities. For this reason, we consider a method, which has been introduced by Bathe for a fluid structure interaction problem.
Subject Maxwell equations, corner singularities, edge finite elements
65N30, 65M25

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