  In this paper we prove the discrete compactness property for a wide class of
p-version finite element approximations of non-elliptic variational eigenvalue
problems in two and three space dimensions. In a very general framework, we
find sufficient conditions for the p-version of a generalized discrete
compactness property, which is formulated in the setting of discrete
differential forms of any order on a d-dimensional polyhedral domain. One of
the main tools for the analysis is a recently introduced smoothed Poincar\'e
lifting operator [M. Costabel and A. McIntosh, On Bogovskii and regularized
Poincar\'e integral operators for de Rham complexes on Lipschitz domains, Math.
Z., (2010)]. For forms of order 1 our analysis shows that several widely used
families of edge finite elements satisfy the discrete compactness property in
p-version and hence provide convergent solutions to the Maxwell eigenvalue
problem. In particular, N\'ed\'elec elements on triangles and tetrahedra (first
and second kind) and on parallelograms and parallelepipeds (first kind) are
covered by our theory.
