In this paper we consider the Maxwell resolvent operator and its finite element
approximation. In this framework it is natural the use of the edge element
spaces and to impose the divergence constraint in a weak
sense with the introduction of a Lagrange multiplier, following
an idea by Kikuchi .
We shall review some of the known properties for edge element
approximations and prove some new result. In particular we shall prove a
uniform convergence in the L
2 norm for the sequence of discrete operators.
These results, together with a general theory introduced by Brezzi, Rappaz and
Raviart , allow an immediate proof of convergence for the
finite element approximation of the time-harmonic