Subdifferential Frictional Contact Problem with Thermo-Electro-Visco-Elastic Locking Materials: Analysis and Approximation

Abstract

This paper investigates a frictional contact problem involving a thermo-electro-visco-elastic model for locking materials in contact with a rigid foundation. Friction is described by the subgradient of a locally Lipschitz function, while contact is governed by Signorini’s unilateral condition. We formulate the problem as a system of three hemivariational inequalities and establish an existence and uniqueness theorem using a fixed-point argument and recent advances in hemivariational inequalities theory. Finally, we present a fully discrete finite element approximation of the model and derive error estimates for the approximate solution.