Bounded penalty method for the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity

Abstract

We consider the bounded penalty method to solve the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity studied in I. El Ouardy, Y. Mandyly, H. Benkhira, and R. Fakhar (2024). We formulate a regularized variational problem and prove the existence and uniqueness of its solution using elliptic quasi-variational inequalities, strongly monotone operators, and Schauder’s fixed point theorem. We also derive error estimates that depend on the penalty parameter ϵ, establishing a convergence rate of \(O(\sqrt{\epsilon})\). Finally, we propose an iterative method to numerically solve the regularized problem and prove its convergence.