Variational and numerical analysis of a quasistatic viscoelastic contact problem with normal compliance and friction

Abstract

In this paper, a class of generalized evolution variational inequalities arising in quasistatic friction contact problem for viscoelastic materials is introduced and studied. Under some suitable assumptions, we obtain an existence and uniqueness theorem of the solution for the generalized evolution variational inequalities by using Banach’s fixed point theorem. Moreover, we study two numerical approximation schemes of the problem: semidiscrete scheme and fully discrete scheme. For both schemes, we prove the existence of the solution and derive the error estimations.

Keywords:

• generalized evolution variational inequality
• semi-discrete scheme
• fully-discrete scheme
• error estimation

AMS Subject Classifications:

• 49J40
• 74D10

Acknowledgments

The authors are grateful to the editor and the referees for their valuable comments and suggestions.