Numerical analysis and simulation of an adhesive contact problem with damage and long memory

This paper studies an adhesive contact model which also takes into account the damage and long memory term. The deformable body is composed of a viscoelastic material process taken as quasistatic. caused by compression or tension involved in constitutive law function modelled through nonlinear parabolic inclusion. Meanwhile, adhesion bonding field on surface while described nonmonotone normal compliance condition. variational formulation governed coupled system consists history-dependent hemivariational inequality for displacement field, ordinary differential equation field. We first consider fully discrete scheme this then focus deriving error estimates numerical solutions. Under appropriate solution regularity assumptions, optimal order estimate derived. At end paper, {we report some two-dimensional simulation results} problem to provide evidence theoretical results.