Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements

By using an inductive procedure we prove that the Galerkin finite element a pproximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec's edge element family on t etrahedral meshes are convergent and free of spurious solutions. This resul t is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can be systematically cons tructed. The tools here developed are used to define a new family of spurio us-free edge elements which, in some sense, are complementary to those defi ned in 1986 by Nedelec.