Hierarchical error estimates for the energy functional in obstacle problems
Please always quote using this URN:urn:nbn:de:0296-matheon-5784
- We present a hierarchical a~posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the energy of the exact solution is, up to data oscillation, equivalent to an appropriate hierarchical estimator. The proof of the main result does not invoke any saturation assumption. Moreover, we prove an a posteriori error estimate indicating that the estimator from \cite{RHWHoppe_RKornhuber_1994a} is asymptotically reliable and we give sufficient conditions for the validity of a saturation assumption. Finally, we corroborate and complement our theoretical results with numerical experiments.
Author: | Qingsong Zou, Andreas Veeser, Ralf Kornhuber, Carsten Gräser |
---|---|
URN: | urn:nbn:de:0296-matheon-5784 |
Referee: | Peter Deuflhard |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2009/03/23 |
Release Date: | 2009/03/23 |
Institute: | Freie Universität Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
Preprint Number: | 575 |