An adaptation of Nitsche's method to the Tresca friction problem

Franz Chouly (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We propose a simple adaptation to the Tresca friction case of the Nitsche-based finite element method given in [Chouly-Hild, 2012, Chouly-Hild-Renard, 2013] for frictionless unilateral contact. Both cases of unilateral and bilateral contact with friction are taken into account, with emphasis on frictional unilateral contact for the numerical analysis. We manage to prove theoretically the fully optimal convergence rate of the method in the H^1(Ω)-norm which is O(h^(1/2+nu)) when the solution lies in H^{3/2+nu}(Ω), 0 < ν ≤ 1/2, in two dimensions and three dimensions, for Lagrange piecewise linear and quadratic finite elements. No additional assumption on the friction set is needed to obtain this proof.

Mots clés: Tresca friction problem; finite elements; Nitsche's method

Domaines: Analyse numérique [math.NA]

Franz Chouly. An adaptation of Nitsche's method to the Tresca friction problem. Journal of Mathematical Analysis and Applications, 2014, 411 (1), pp.329-339. ⟨hal-00783827⟩