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We consider a fully-discrete approximations of 1-D heat equation with dynamicboundary conditions for which we provide a controllability result. The proof ofthis result is based on a relaxed observability inequality for thecorresponding adjoint system. This is done by using a suitable Carlemanestimate for such models where the discrete parameters $h$ and $\Delta t$ areconnected to the one of the large Carleman parameters.

Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions