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Article Dans Une Revue Computers & Mathematics with Applications Année : 2022

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

Résumé

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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Dates et versions

hal-03354078 , version 1 (24-09-2021)

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Citer

Daniele Antonio Di Pietro, Ilaria Fontana, Kyrylo Kazymyrenko. A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method. Computers & Mathematics with Applications, 2022, 111, pp.61-80. ⟨10.1016/j.camwa.2022.02.008⟩. ⟨hal-03354078⟩
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