Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear. (1st September 2020)

• Record Type: Journal Article
• Authors: Chen, Tao; Huang, Nan-jing; Xiao, Yi-bin
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 2003
• Page End: 2031
• Publication Date: 2020-09-01
• Subjects: Viscoelastic contact -- frictional contact -- hyperbolic quasi-variational inequality -- fully discrete scheme -- error estimate; 74M15 -- 74M10 -- 49J40 -- 74G25 -- 74G30 -- 65N30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1712394
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational inequality by employing the variational method. We adopt the Rothe method to show the existence and uniqueness of solution for the hyperbolic quasi-variational inequality under mild conditions. We also give a fully discrete scheme for solving the hyperbolic quasi-variational inequality and obtain error estimates for the fully discrete scheme.