In this paper, efficient algorithms for contact problems with Tresca and
Coulomb friction in three dimensions are presented and analyzed. The numerical
approximation is based on mortar methods for nonconforming meshes with dual Lagrange
multipliers. Using a nonsmooth complementarity function for the 3D friction
conditions, a primal-dual active set algorithm is derived. The method determines
active contact and friction nodes and, at the same time, resolves the additional
nonlinearity originating from sliding nodes. No regularization and no penalization
is applied, and local superlinear convergence can be observed. In combination with
a multigrid method, it defines a robust and fast strategy for contact problems with
Tresca or Coulomb friction. The efficiency and flexibility of the method is illustrated
by several numerical examples.Deutsche Forschungsgemeinschaft, SFB 404, B8, SPP 114
