Numerical analysis of a thermal frictional contact problem with long memory

The objective in this paper is to study a thermal frictional contact model. The deformable body consists of viscoelastic material and the process assumed be dynamic. It that behaves accordance with Kelvin-Voigt constitutive law effect added. variational formulation model leads coupled system including history-dependent hemivariational inequality for displacement field an evolution equation temperature field. In system, we first consider fully discrete scheme it then focus on deriving error estimates numerical solutions. Under appropriate assumptions solution regularity, optimal order estimate obtained. At end manuscript, report some simulation results problem so as verify theoretical results.