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Mathematics of Computation

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A posteriori error estimator and error control for contact problems


Authors: Alexander Weiss and Barbara I. Wohlmuth
Journal: Math. Comp. 78 (2009), 1237-1267
MSC (2000): Primary 65N30, 65N15, 65N50
DOI: https://doi.org/10.1090/S0025-5718-09-02235-2
Published electronically: February 20, 2009
MathSciNet review: 2501049
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Abstract: In this paper, we consider two error estimators for one-body contact problems. The first error estimator is defined in terms of $ H($div$ )$-conforming stress approximations and equilibrated fluxes while the second is a standard edge-based residual error estimator without any modification with respect to the contact. We show reliability and efficiency for both estimators. Moreover, the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order. The second estimator is used in a control-based AFEM refinement strategy, and the decay of the error in the energy is shown. Several numerical tests demonstrate the performance of both estimators.


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Additional Information

Alexander Weiss
Affiliation: Institute of Applied Analysis and Numerical Simulations (IANS), Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Email: weiss@ians.uni-stuttgart.de

Barbara I. Wohlmuth
Affiliation: Institute of Applied Analysis and Numerical Simulations (IANS), Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Email: wohlmuth@ians.uni-stuttgart.de

DOI: https://doi.org/10.1090/S0025-5718-09-02235-2
Keywords: Equilibrated fluxes, Lagrange multipliers, a posteriori error estimates, contact problems
Received by editor(s): July 17, 2007
Received by editor(s) in revised form: June 2, 2008
Published electronically: February 20, 2009
Additional Notes: This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, B8
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.