Uzawa block relaxation domain decomposition method for the two-body contact problem with Tresca friction

We propose a Uzawa block relaxation domain decomposition method for a two-body contact problem with Tresca friction. We introduce auxiliary interface unknowns to transform the variational problem into a saddle-point problem. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two uncoupled linear elasticity subproblems in each iteration. The auxiliary unknowns are computed explicitly using Kuhn–Tucker conditions and Fenchel duality theory. Numerical experiments show the scalability of the domain decomposition algorithm on matching or nonmatching meshes for two- or three-dimensional contact problems.