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Efficient Algorithms for Problems with Friction

In this paper, a nonconforming discretization method for the frictional contact between two bodies subjected to antiplane shear deformation is considered. The method is based on a mixed variational formulation where dual basis functions are used for the discretization of the Lagrange multiplier. Under some regularity assumptions on the solution, an optimal a priori error estimate is obtained. To solve the discrete nonlinear problem an inexact primal-dual active set strategy is introduced. Finally, numerical examples confirming the theoretical result for the a priori error estimate and illustrating the performance of the algorithm are presented. The results can easily be generalized to the case of Coulomb friction. For this case a numerical example is given.