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A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method

Abstract : We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed upper bound for the dual norm of the residual. This norm is shown to control the natural energy norm up to a boundary term, which can be removed under a saturation assumption. The basic estimate is then refined to distinguish the different components of the error, and is used as a starting point to design an algorithm including adaptive stopping criteria for the nonlinear solver and automatic tuning of a regularization parameter. We then discuss an actual way of computing the stress reconstruction based on the Arnold-Falk-Winther finite elements. Finally, after briefly discussing the efficiency of our estimators, we showcase their performance on a panel of numerical tests.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03354078
Contributor : Ilaria Fontana Connect in order to contact the contributor
Submitted on : Friday, September 24, 2021 - 3:54:49 PM
Last modification on : Wednesday, January 5, 2022 - 11:04:02 PM

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NitscheNoFriction.pdf
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  • HAL Id : hal-03354078, version 1

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Daniele Antonio Di Pietro, Ilaria Fontana, Kyrylo Kazymyrenko. A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method. 2021. ⟨hal-03354078⟩

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