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

• Published in: Computer methods in applied mechanics and engineering Vol. 425; p. 116950
• Main Authors: Fontana, Ilaria, Di Pietro, Daniele A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.05.2024; Elsevier
• Subjects: A posteriori error estimate; Adaptive algorithms; Arnold–Falk–Winther mixed finite element; Equilibrated stress reconstruction; Frictional unilateral contact problem; Mathematics; Numerical Analysis; Weakly enforced contact conditions; 65N15; 74S05; Frictional unilateral contact problem; A posteriori error estimate; Adaptive algorithms; 65N50; Arnold–Falk–Winther mixed finite element; Equilibrated stress reconstruction; 74M15; 65N30; Weakly enforced contact conditions; Arnold-Falk-Winther mixed finite element
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2024.116950

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.