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Mustapha Bouallala, EL Hassan Essoufi, Abdelhafid Ouaanabi, Youssef Ouafik, Variational analysis and numerical simulation for a dynamic contact problem with Coulomb’s friction in thermo-viscoelasticity

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DOI: 10.23952/asvao.8.2026.2.02
Volume 8, Issue 2, 1 August 2026, Pages 147-166

 

Abstract. The focus of this study is a dynamic frictional contact model involving a viscoelastic body with thermal effects and a conductive foundation. Coulomb’s law describes the frictional behavior, while a normal compliance model simulates the contact. We derive a variational formulation for the problem and establish the existence of a unique weak solution by using the Banach fixed point theorem. To solve the problem, we propose a fully discrete scheme that combines the finite element method for spatial approximation with the Euler scheme for the time discretization. Error estimates for the solutions are derived, and linear convergence is achieved under suitable regularity assumptions. Finally, numerical simulations are presented to demonstrate the performance of the proposed method.

 

How to Cite this Article:
M. Bouallala, E.H. Essoufi, A. Ouaanabi, Y. Ouafik, Variational analysis and numerical simulation for a dynamic contact problem with Coulomb’s friction in thermo-viscoelasticity, Appl. Set-Valued Anal. Optim. 8 (2026), 147-166.