Existence of a Fixed Point of a Nonsmooth Function Arising in Numerical Mechanics
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A recent work (Acary et al. 2010) introduces a formulation as a nonsmooth fixed-point problem of a basic problem in numerical mechanics (namely the dynamical Coulomb friction problem in finite dimension with discretized time). Using this new formulation, the existence of a solution to the problem and its numerical resolution are then guaranteed under a strong assumption on the data of this problem. In this paper, we show that the fixed point problem admits solution under a natural, weaker assumption. This existence proof uses a perturbation argument combined with continuity properties of a set-valued mapping associated with the constraints of the problem.
KeywordsNonsmooth analysis Numerical mechanics Second-order cone programming Sensitivity analysis Fixed point
Mathematics Subject Classifications (2010)49J52 70F40 90C25
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