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A posteriori error control of finite element approximations for Coulomb’s frictional contact. (English) Zbl 1032.74050
The paper studies a frictional unilateral contact problem governed by Coulomb’s law. Two mixed finite element methods are proposed, and the existence of solutions and properties of discrete solutions are studied. An a posteriori error estimator based on the concept of error in constitutive relations allows to quantify the accuracy of finite element approximations. Related results can be found in [P. Coorevits, P. Hild, and J.-P. Pelle, Comput. Methods Appl. Mech. Engrg. 186, 65-83 (2000; Zbl 0979.74066) and P. Ladeveze and D. Leguillon, SIAM J. Numer. Anal. 20, 485-509 (1983; Zbl 0582.65078)]. Several numerical studies are performed in which the estimator is computed and coupled with a mesh-adaptive procedure.

74S05 Finite element methods applied to problems in solid mechanics
74M10 Friction in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
74M15 Contact in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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