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On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation

F. Ben BelgacemC. BernardiA. BlouzaM. Vohralík — 2009

Mathematical Modelling of Natural Phenomena

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 discrete problem...

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