Publication Date:
2011-02-21
Description:
We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞ -error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates. Content Type Journal Article Pages 1-14 DOI 10.1007/s00211-011-0360-9 Authors C. Ortner, Mathematical Institute, University of Oxford, 24–29 St. Giles’, Oxford, OX1 3LB UK W. Wollner, Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, INF 294, 69120 Heidelberg, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X
Print ISSN:
0029-599X
Electronic ISSN:
0945-3245
Topics:
Mathematics
