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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.

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Metadaten
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
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