African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 252

Full Length Research Paper

Convergences and numerical analysis of a contact problem with normal compliance and unilateral constraint

Yahyeh Souleiman
  • Yahyeh Souleiman
  • Mathematics and Computer Science Laboratory, University of Djibouti, Campus Balbala, Djibouti.
  • Google Scholar


  •  Received: 30 September 2020
  •  Accepted: 05 January 2021
  •  Published: 30 June 2021

Abstract

This paper represents a continuation of a previous study on “Analysis of a Sliding Frictional Contact Problem with Unilateral Constraint”. This study considers a mathematical model which describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraints, associated to a sliding version of Coulomb’s law of dry friction. After a description of the model, the variational formulation was presented. Then, the dependence of the solution was studied with respect to the data and a convergence result was proven. Regularization method was also used to study the existence and uniqueness of the contact problem for which a convergence result was presented. Finally, a semi-discrete scheme was introduced for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, an optimal order error estimate was derived.

Key words: Elastic material, frictional contact, normal compliance, unilateral constraint, variational formulation, weak solution, regularization method, finite element, error estimate.