Hild, Patrick; Renard, Yves An error estimate for the Signorini problem with Coulomb friction approximated by finite elements. (English) Zbl 1146.74050 SIAM J. Numer. Anal. 45, No. 5, 2012-2031 (2007). Summary: The paper is concerned with the unilateral contact model and Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the contact zone. A convenient discrete contact and friction condition is introduced in order to perform a convergence study. We finally obtain a first a priori error estimate under the assumptions ensuring the uniqueness of the solution to the continuous problem. Cited in 15 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 74M15 Contact in solid mechanics 74M10 Friction in solid mechanics 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:unilateral contact; uniqueness; a priori error estimate PDFBibTeX XMLCite \textit{P. Hild} and \textit{Y. Renard}, SIAM J. Numer. Anal. 45, No. 5, 2012--2031 (2007; Zbl 1146.74050) Full Text: DOI HAL