Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear. (1st September 2020) - Chen, Tao; Huang, Nan-jing; Xiao, Yi-bin
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.