Approximation of the Telegrapher´s equations

The problem of approximating a distributed parameter system with free boundary conditions is solved for the 1-dimensional Telegrapher´s equations. The Telegrapher´s equations are described using an infinite-dimensional port-Hamiltonian model, and we derive a finite dimensional port-Hamiltonian model using a mixed finite-element procedure. We show that energy conservation, passivity and some dynamic invariants are preserved in the discretization.