Convergence analysis for hyperbolic evolution problems in mixed form

In this paper we present a convergence analysis for the space discretization of hyperbolic evolution problems in mixed form. The results of [1] are extended to this situation, showing the relationships between the approximation of the underlying eigenvalue problem and the space discretization of the corresponding evolution problem. The theory is applied to the finite element approximations of the wave equation in mixed form and to the Maxwell’s equations. Some numerical results confirm the theory and make clear the critical points.