1.Fakult?t für Mathematik,Universit?t Duisburg-Essen,Duisburg,Germany;2.Johann Radon Institute for Computational and Applied Mathematics (RICAM),Austrian Academy of Sciences,Linz,Austria
Abstract:
We discuss the full discretization of an elliptic optimal control problem with pointwise control and state constraints. We provide the first reliable a-posteriori error estimator that contains only computable quantities for this class of problems. Moreover, we show, that the error estimator converges to zero if one has convergence of the discrete solutions to the solution of the original problem. The theory is illustrated by numerical tests.