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

We consider the finite- element approxim ation of a distributed optimal control problem govemed by a semilinea r ellip­ tic partial differential equation, where pointwise constraints on the control are given. We prove the existence of local approximate so­ lutions converging to a given lo cal reference solu tion. Moreover, we derive error estimates for local solutions in the maximum nonn.