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The finite element approximation of optimal control problems for semilin- ear elliptic partial dierential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the do- main. Under the standard linear independency condition on the active gradients and a strong second-order sucient optimality condition, optimal error estimates are derived for locally optimal controls.

modélisation mathématique et analyse numérique

Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space