On the dynamic frictionless contact problem with normal compliance in thermo-piezoelectricity

In this work, we study, from a variational and numerical point of view, a dynamic contact problem between a thermo-electro-viscoelastic body and an electrically and thermally conductive foundation. The normal compliance condition and a nonlinear regularized electrical and thermal conditions are employed to model the contact. We provide existence and uniqueness results of a weak solution to the model using adequate auxiliary problems, Gronwall’s lemma, and Banach fixed point theorem. Finally, we introduce a fully discrete approximation using the finite element method and an Euler scheme. Then we derive some error estimates, leading to the linear convergence result under suitable additional regularity conditions.