Analysis and numerical simulation of frictionless contact problem with normal compliance in thermo-viscoelasticity

This article is concerned with the existence and uniqueness of results and the numerical modeling of a frictionless contact problem between a thermo-viscoelastic body and a rigid boundary condition. The contact is described by the normal compliance condition. We derive a weak formulation of the model and prove the existence of a unique weak solution using the Galerkin method and the Banach fixed point theorem. The fully discrete finite element scheme of the weak formulation is introduced, and error estimates for the approximate solution are derived. We present and study a successive iterative (decomposition) method to solve two sub-problems for the displacement field and the temperature sequentially. Finally, we present the results of the numerical simulations, demonstrating the method’s performance.