Error Estimates for the Finite Element Solution of Variational Inequalities. Part I. Primal Theory.

F. Brezzi; W.W. Hager; P.A. Raviart

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The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the...