On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Technische Universität Berlin, Fakultät II – Mathematik und Naturwissenschaften, Str. des 17. Juni 136, 10623 Berlin, Germany. neitzel@math.tu-berlin.de; troeltz@math.tu-berlin.de

Received: 10 January 2007
Revised: 31 July 2007
Revised: 23 October 2007

Abstract

In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.