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A Convergence Criterion for a Class of Stationary Inclusions in Hilbert Spaces
Version 1
: Received: 7 December 2023 / Approved: 7 December 2023 / Online: 8 December 2023 (08:02:46 CET)
A peer-reviewed article of this Preprint also exists.
Sofonea, M.; Tarzia, D.A. A Convergence Criterion for a Class of Stationary Inclusions in Hilbert Spaces. Axioms 2024, 13, 52. Sofonea, M.; Tarzia, D.A. A Convergence Criterion for a Class of Stationary Inclusions in Hilbert Spaces. Axioms 2024, 13, 52.
Abstract
We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.
Keywords
stationary inclusion; projection operator; convergence criterion; convergence results; penalty method, frictional contact problem; elastic constitutive law
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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