A posteriori error estimator and error control for contact problems

Weiss, Alexander; Wohlmuth, Barbara

doi:10.1090/S0025-5718-09-02235-2

A posteriori error estimator and error control for contact problems
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by Alexander Weiss and Barbara I. Wohlmuth;

Math. Comp. 78 (2009), 1237-1267

DOI: https://doi.org/10.1090/S0025-5718-09-02235-2

Published electronically: February 20, 2009

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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 $H(\text {div})$-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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