Mathematics

The resonant modes of time harmonic Maxwell equations can be identified with the eigensolutions of a problem represented by a variational formulation in mixed form.  In this talk we review the finite element approximation of eigenvalue problems arising from partial differential equations. In particular, it will be shown that the analysis of mixed problems differs significantly from that of standard Galerkin formulations. We will show how these results can be applied to the a priori analysis  of Maxwell's eigenvalue problem and we will give some indications on how the a posteriori analysis can be performed.