Well-posed constrainted problems with applications in contact mechanics. (August 2023) - Barboteu, Mikael; Sofonea, Mircea
Abstract: We consider an abstract problem P K in the framework of a normed space, associated to a set of constraints K . We use the concept of T -well-posedness to deduce various convergence results to the unique solution of P K . We illustrate our abstract results in the study two representative nonlinear problems: a minimization problem and a second kind elliptic variational inequality, both in the framework of reflexive Banach spaces. Finally, we consider a static contact model with elastic materials which leads to a weak formulation in terms of a variational inequality for the displacement field. We specify the corresponding convergence results, give their numerical validation and provide various mechanical interpretations.