Variational and Numerical Analysis for Frictional Contact Problem with Normal Compliance in Thermo-Electro-Viscoelasticity

In this paper, we consider a mathematical model of a contact problem in thermo-electro-viscoelasticity with the normal compliance conditions and Tresca’s friction law. We present a variational formulation of the problem, and we prove the existence and uniqueness of the weak solution. We also study the numerical approach using spatially semidiscrete and fully discrete finite element schemes with Euler’s backward scheme. Finally, we derive error estimates on the approximate solutions.