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

Ilaria Fontana (1) , Daniele A. Di Pietro (2)

1 Northwestern University [Evanston]
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: Frictional unilateral contact problem; Weakly enforced contact conditions; A posteriori error estimate; Equilibrated stress reconstruction; Arnold-Falk-Winther mixed finite element; Adaptive algorithms

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

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⟩