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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A posteriori error estimator and error control for contact problems
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by Alexander Weiss and Barbara I. Wohlmuth PDF
Math. Comp. 78 (2009), 1237-1267 Request permission

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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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
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 1237-1267
  • MSC (2000): Primary 65N30, 65N15, 65N50
  • DOI: https://doi.org/10.1090/S0025-5718-09-02235-2
  • MathSciNet review: 2501049