Discrete Carleman Estimates and Application to Controllability for a Fully-Discrete Parabolic Operator with Dynamic Boundary Conditions

We consider a fully-discrete approximation of a 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding adjoint system. This is conducted using a suitable Carleman estimate for such models where the discrete parameters h and Δt are connected to one of the large Carleman parameters. © 2023 Elsevier Inc.