  In this contribution, we extend the hybridization framework for the Hodge
Laplacian [Awanou et al., Hybridization and postprocessing in finite element
exterior calculus, 2023 ] to port-Hamiltonian systems describing linear wave
propagation phenomena. To this aim, a dual field mixed Galerkin discretization
is introduced, in which one variable is approximated via conforming finite
element spaces, whereas the second is completely local. This scheme is
equivalent to the second order mixed Galerkin formulation and retains a
discrete power balance and discrete conservation laws. The mixed formulation is
also equivalent to the hybrid formulation. The hybrid system can be efficiently
solved using a static condensation procedure in discrete time. The size
reduction achieved thanks to the hybridization is greater than the one obtained
for the Hodge Laplacian as one field is completely discarded. Numerical
experiments on the 3D wave and Maxwell equations show the convergence of the
method and the size reduction achieved by the hybridization.
