An error estimate for the Signorini problem with Coulomb friction approximated by finite elements

Patrick Hild (1) , Yves Renard (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 MIP - Mathématiques pour l'Industrie et la Physique

The present paper is concerned with the unilateral contact model and the 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.

Mots clés: uniqueness of solution; Coulomb friction; unilateral contact; finite elements; a priori error estimate

Domaines: Analyse numérique [math.NA]

Patrick Hild, Yves Renard. An error estimate for the Signorini problem with Coulomb friction approximated by finite elements. SIAM Journal on Numerical Analysis, 2007, 45 (5), pp.2012-2031. ⟨10.1137/050645439⟩. ⟨hal-00690597⟩