An adaptation of Nitsche’s method to the Tresca friction problem. (English) Zbl 1311.74112

Summary: We propose a simple adaptation to the Tresca friction case of the Nitsche-based finite element method introduced previously 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 \(H^1(\Omega)\)-norm which is \(O(h^{\frac{1}{2}+\nu})\) when the solution lies in \(H^{\frac{3}{2}+\nu}(\Omega)\), \(0<\nu\leqslant k-1/2\), in two dimensions and three dimensions, for Lagrange piecewise linear \((k=1)\) and quadratic \((k=2)\) finite elements. No additional assumption on the friction set is needed to obtain this proof.


74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q74 PDEs in connection with mechanics of deformable solids
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