M 614/616

In this talk we will consider barrier and penalty methods for the solution of optimization problems governed by partial differential equations (PDEs) with additional pointwise constraints on the solution of the PDE. The introduction of a barrier or penalty term for the latter reduces the problem to a simple (regularized) PDE constrained optimization problem but introduces an additional error. We will discuss the convergence behavior of the regularized solutions to those of the unregularized problem. This motivates the need to adjust the regularization and discretization error by means of a posteriori error stimates. We will discuss the derivation of these error estimates and show some numerical results regarding the sharpness of the estimates.

JProf. Dr. Winnifried Wollner

Universität Hamburg