We study Dirichlet and Neumann control problems associated to a semilinear elliptic equation defined in a curved domain Ω. To deal with the numerical analysis of these problems, the approximation of Ω by an appropriate domain Ωh (typically polygonal) is required. Here we formulate the corresponding infinite dimensional control problems in Ωh and we study the influence of the replacement of Ω by Ωh on the solutions of the control problems. Our goal is to derive some error estimates between the solutions defined on Γ = ∂Ω with those defined on Γh = ∂Ωh.

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