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Error estimates for the finite-element approximation of a semilinear elliptic control problem

Casas, Eduardo; Tröltzsch, Fredi

Inst. Mathematik

We consider the finite-element approximation of a distributed optimal control problem governed by a semilinear elliptic partial differential equation, where pointwise constraints on the control are given. We prove the existence of local approximate solutions converging to a given local reference solution. Moreover, we derive error estimates for local solutions in the maximum norm.