Finite-difference discretizations of quadratic control problems governed by ordinary elliptic differential equations

Authors:
Walter Alt;Nils Bräutigam
Affiliations:
Institut für Angewandte Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany 07743;Institut für Angewandte Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany 91058
Venue:
Computational Optimization and Applications
Year:
2009

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Abstract

In this paper, we analyze finite difference discretizations for a class of control constrained elliptic optimal control problems. If the optimal control has a derivative of bounded variation, we show discrete quadratic convergence in terms of the mesh size h of the discrete optimal controls. Furthermore, based on the optimality conditions, we construct a new discrete control for which we derive continuous error estimates of order h 2.