Analysis of a contact problem in thermoviscoelasticity under the Green–Lindsay model

In this article, we consider a one-dimensional contact problem in generalized thermoviscoelasticity based on the Green–Lindsay theory. We prove that the energy associated to the system decays exponentially to zero and we analyze a finite element approximation. It is shown that if the continuous solution is sufficiently smooth then the error in the L2L2-norm is order of h+Δth+Δt. Furthermore, we demonstrate that the discrete energy decays as the time increases.