Boundary observability of a numerical approximation scheme of Maxwell's system in a cube

We consider a numerical space discretization of Maxwell’s system by the socalled Yee’s scheme. For such a scheme, we first show that the boundary observability estimate is not uniform with respect to the mesh size. Using a discrete multiplier method, we prove an observability estimate that separates the low and high frequency contributions. We then describe one of its consequence to control problem, namely the Tychonoff regularization technique that shows that the discrete system with a discrete boundary control with additional internal controls (tending to zero as the mesh size goes to zero) converges to the continuous system with a boundary control.