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Analysis and numerical approximation of a dynamic contact problem with friction and adhesion

Volume 45 / 2018

Abderrezak Kasri, Arezki Touzaline Applicationes Mathematicae 45 (2018), 103-127 MSC: 47J20, 65M60, 74M10, 74M15. DOI: 10.4064/am2323-6-2017 Published online: 15 January 2018

Abstract

We study a dynamic contact problem for viscoelastic materials with long-term memory. The contact is modelled with a coupled system of Tresca’s friction law and an ordinary differential equation which describes the adhesion effect. Under appropriate assumptions, we provide a weak formulation of the mechanical problem and establish the existence and uniqueness of a weak solution. We then introduce a fully discrete scheme for the model. We derive error estimates, and under suitable regularity assumptions we derive a linear convergence result.

Authors

  • Abderrezak KasriDépartement de Mathématiques
    Université 20 Août 1955 – Skikda
    B.P. 26, Route El-Hadaiek
    Skikda, Algeria
    e-mail
  • Arezki TouzalineLaboratoire de Systèmes Dynamiques
    Faculté de Mathématiques
    USTHB
    B.P. 32, El Alia
    Bab-Ezzouar, 16111 Alger, Algeria
    e-mail

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