Fixed point strategies for elastostatic frictional contact problems

Patrick Laborde (1) , Yves Renard (2)

1 EPOC - Environnements et Paléoenvironnements OCéaniques
2 ICJ - Institut Camille Jordan

Several fixed point strategies and Uzawa algorithms (for classical and augmented Lagrangian formulations) are presented to solve the unilateral contact problem with Coulomb friction. These methods are analyzed, without introducing any regularization, and a theoretical comparison is performed. Thanks to a formalism coming from convex analysis, some new fixed point strategies are presented and compared to known methods. The analysis is first performed on continuous Tresca problem and then on the finite dimensional Coulomb problem derived from an arbitrary finite element method.

Mots clés: unilateral contact; Coulomb friction; Tresca problem; Signorini problem; bipotential; fixed point; Uzawa algorithm

Domaines: Analyse numérique [math.NA]

Patrick Laborde, Yves Renard. Fixed point strategies for elastostatic frictional contact problems. Mathematical Methods in the Applied Sciences, 2008, 31, pp.415-441. ⟨10.1002/mma.921⟩. ⟨hal-01330376⟩