Well-posed constrainted problems with applications in contact mechanics. (August 2023)

• Record Type: Journal Article
• Authors: Barboteu, Mikael; Sofonea, Mircea
• Is Part Of: Nonlinear analysis. Volume 72(2023)
• Publication Date: 2023-08
• Subjects: Well-posed constrainted problem -- Tykhonov triple -- Variational inequality -- Contact model -- Numerical approximation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2023.103841
• Languages: English
• ISSNs: 1468-1218

Abstract

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.