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Efficient and reliable hierarchical error estimates for the discretization error of elliptic obstacle problems


Authors: Ralf Kornhuber and Qingsong Zou
Journal: Math. Comp. 80 (2011), 69-88
MSC (2010): Primary 65N15, 65N30
Published electronically: June 23, 2010
MathSciNet review: 2728972
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Abstract: We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.


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Additional Information

Ralf Kornhuber
Affiliation: Freie Universität Berlin, Institut für Mathematik, Arnimallee 6, D-14195 Berlin, Germany
Email: kornhuber@math.fu-berlin.de

Qingsong Zou
Affiliation: University Guangzhou, Department of Scientific Computation and Computer Applications, Guangzhou, 510275, People’s Republic of China
Email: mcszqs@mail.sysu.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-2010-02394-4
Received by editor(s): September 17, 2008
Received by editor(s) in revised form: June 22, 2009
Published electronically: June 23, 2010
Additional Notes: The authors gratefully acknowledge substantial support by Carsten Gräser and Oliver Sander through fruitful discussions and numerical assistance. The second author is supported in part by NSFC under the grant 10601070 and in part by Alexander von Humboldt Foundation hosted by Freie Universität in Berlin.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.