Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments

Franz Chouly (1) , Patrick Hild (2) , Yves Renard (3, 4, 5)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
4 ICJ - Institut Camille Jordan
5 MMCS - Modélisation mathématique, calcul scientifique

A general Nitsche method, which encompasses symmetric and non-symmetric variants, is proposed for frictionless unilateral contact problems in elasticity. The optimal convergence of the method is established both for two and three-dimensional problems and Lagrange affine and quadratic finite element methods. Two and three-dimensional numerical experiments illustrate the theory.

Keywords: finite elements; unilateral contact; Nitsche's method

Domains: Numerical Analysis [math.NA]

Franz Chouly, Patrick Hild, Yves Renard. Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments. Mathematics of Computation, 2015, 84, pp.1089-1112. ⟨10.1090/S0025-5718-2014-02913-X⟩. ⟨hal-00776619⟩