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The virtual element method for a contact problem with wear and unilateral constraint

Published: 01 December 2024 Publication History

Abstract

This paper is dedicated to the numerical solution of a mathematical model that describes frictional quasistatic contact between an elastic body and a moving foundation, with the wear effect on the contact interface of the moving foundation due to friction. The mathematical problem is a system consisting of a time-dependent quasi-variational inequality and an integral equation. The numerical method is based on the use of the virtual element method (VEM) for the spatial discretization of the variational inequality and a variable step-size left rectangle integration formula for the integral equation. The existence and uniqueness of a numerical solution are shown, and optimal order error estimates are derived for both the displacement and the wear function for the lowest order VEM. Numerical results are presented to demonstrate the efficiency of the method and to illustrate the numerical convergence orders.

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Information

Published In

cover image Applied Numerical Mathematics
Applied Numerical Mathematics  Volume 206, Issue C
Dec 2024
358 pages

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 December 2024

Author Tags

  1. 65N30
  2. 49J40

Author Tags

  1. Frictional contact
  2. Wear
  3. Quasi-variational inequality
  4. Virtual element method
  5. Error estimates

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