  In this paper we consider the numerical solution of the Hamiltonian wave
equation in two spatial dimension. We use the Mimetic Finite Difference (MFD)
method to approximate the continuous problem combined with a symplectic
integration in time to integrate the semi-discrete Hamiltonian system. The main
characteristic of MFD methods, when applied to stationary problems, is to mimic
important properties of the continuous system. This approach, associated with a
symplectic method for the time integration yields a full numerical procedure
suitable to integrate Hamiltonian problems. A complete theoretical analysis of
the method and some numerical simulations are developed in the paper.
