SUMMARYA scalar contact problem with friction governed by the Yukawa equation is reduced to a boundary variational inequality. The presence of the non-di erentiable friction functional causes some di culties when approximated. We present two methods to overcome this di culty. The ÿrst one is a regularization leading to a non-linear boundary variational equation, for which we propose an iterative procedure, whereas the second method is based on the boundary mixed variational formulation involving Lagrange multipliers. We propose Uzawa's algorithm to compute the saddle point of the corresponding boundary Lagrangian and investigate the discretization of various formulations by the boundary element Galerkin method. Convergence of the boundary element solution is proved and a convergence order is obtained.
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