  The anisotropic and heterogeneous $N$-dimensional wave equation, controlled
and observed at the boundary, is considered as a port-Hamiltonian system. A
recent structure-preserving mixed Galerkin method is applied, leading directly
to a finite-dimensional port-Hamiltonian system: its numerical analysis is
carried out in a general framework. Optimal choices of mixed finite elements
are then proved to reach the best trade-off between the convergence rate and
the number of degrees of freedom for the state error. Exta compatibility
conditions are identified for the Hamiltonian error to be twice that of the
state error, and numerical evidence is provided that some combinations of
finite element families meet these conditions. Numerical simulations in 2D are
performed to illustrate the main theorems among several choices of classical
finite element families. Several test cases are provided, including non-convex
domain, anisotropic or hetergoneous cases and absorbing boundary conditions.
