Boundary observability for the space semi-discretizations of the wave equation
Boundary observability for the space semi-discretizations of the 1 – d wave equation
We consider space semi-discretizations of the 1- wave equation in a bounded interval with homogeneous Dirichlet boundary conditions. We analyze the problem of boundary observability, , the problem of whether the total energy of solutions can be estimated uniformly in terms of the energy concentrated on the boundary as the net-spacing → 0. We prove that, due to the spurious modes that the numerical scheme introduces at high frequencies, there is no such a uniform bound. We prove however a uniform...
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