Self-adaptive projection and boundary element methods for contact problems with Tresca friction

A self-adaptive projection method is considered for the numerical simulation of contact problems with Tresca friction. The contact constraints are imposed in the fixed point formulation using projection operators. It leads to a projection method where each iterative step consists of a linear elasticity problem with Robin conditions on the contact boundary. To ensure the efficiency of the method, a self-adaptive rule is given to adjust the parameter automatically. We prove the convergence of the method in function space and demonstrate its application with the boundary element method. The numerical experiments are presented to show the performance of the proposed method.