a1 Chemnitz University of Technology, Faculty of Mathematics, 09107 Chemnitz, Germany.
a2 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrae 69, 4040 Linz, Austria. firstname.lastname@example.org
Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical experiments.
(Received August 27 2009)
(Revised February 9 2010)
(Revised May 18 2010)
(Online publication August 06 2010)
Mathematics Subject Classification: