Numerical Studies of a Class of Thermoviscoelastic Frictional Contact Problem Described by Fractional Differential Hemivariational Inequalities

The intention of our study is to investigate a thermoviscoelastic frictional contact problem involving time-fractional order operators and long memory effects. Both the Kelvin-Voigt constitutive law and the heat conduction equation incorporate time-fractional characteristics. The model's variational formulation yields a coupled system consisting of a history-dependent hemivariational inequality governing the displacement field along with an evolution equation describing the temperature field. The existence of a unique weak solution is established by using Banach fixed point theory and some results on hemivariational inequalities. Subsequently, we present a fully discretized scheme and pay attention to the derivation of error estimates for the numerical solutions. The attainment of an optimal order error estimate is achieved under a few solution regularity assumptions. Numerical simulations are conducted at the end of this manuscript to validate our theoretical findings.