Preprint 21-2003

Error estimates for the numerical approximation of boundary semilinear elliptic control problems

Author(s) : Eduardo Casas , Mariano Mateos , Fredi Tröltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 21-2003

MSC 2000

49K20 Problems involving partial differential equations

49N10 Linear-quadratic problems

90C46 Optimality conditions, duality

49M20 Methods of relaxation type

Abstract :
We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, error estimates are established.

Keywords : boundary control, semilinear elliptic equation, numerical approximation, error estimates