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

Source file is available as :   Postscript Document

Author(s) : Eduardo Casas , Fredi Tröltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 748-2002

MSC 2000

49J20 Optimal control problems involving partial differential equations
49K20 Problems involving partial differential equations
49M05 Methods based on necessary conditions
65K10 Optimization and variational techniques

Abstract :
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.