Control and Cybernetics

vol. 37 (2008) No. 2 On the regularization error of state onstrained Neumann ontrol problems∗ by Klaus Krumbiegel and Arnd Rös h Universität Duisburg-Essen, Department of Mathemati s Forsthausweg 2, D-47057 Duisburg, Germany e-mail: klaus.krumbiegel uni-due.de; arnd.roes h uni-due.de Abstra t: A linear ellipti optimal ontrol problem with pointwise state onstraints in the interior of the domain is onsidered. Furthermore, the ontrol is given on the boundary with asso iated onstraints. An arti ial distributed ontrol is introdu ed in the ost fun tional, in the state equation and in the state onstraints. Sin e there are no ontrol onstraints for the arti ial ontrol, e ient numeri al methods an be easily established. Based on a possible violation of the pure pointwise state onstraints, an error estimate for the regularization error is derived. The theoreti al results are illustrated by numeri al tests.