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Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2024

An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact

Ilaria Fontana
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Abstract

We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an equilibrated stress reconstruction in the Arnold-Falk-Winther space that includes a guaranteed upper bound distinguishing the different components of the error. This analysis is the starting point for the development of an adaptive algorithm including a stopping criterion for the generalized Newton method. This algorithm is then used to perform numerical simulations that validate the theoretical results.
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Dates and versions

hal-04375623 , version 1 (05-01-2024)

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Ilaria Fontana, Daniele A. Di Pietro. An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact. Computer Methods in Applied Mechanics and Engineering, 2024, 425, pp.116950. ⟨10.1016/j.cma.2024.116950⟩. ⟨hal-04375623⟩
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