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Using uniform global Carleman estimates for discrete elliptic andsemi-discrete hyperbolic equations, we study Lipschitz and logarithmicstability for the inverse problem of recovering a potential in a semi-discretewave equation, discretized by finite differences in a 2-d uniform mesh, fromboundary or internal measurements. The discrete stability results, whencompared with their continuous counterparts, include new terms depending on thediscretization parameter h. From these stability results, we design a numericalmethod to compute convergent approximations of the continuous potential.

Stability of an inverse problem for the discrete wave equation and convergence results