Variational and Numerical Analysis of a Dynamic Tresca Frictional Contact Problem for Thermo‐Electro‐Viscoelastic Materials

ABSTRACT This paper addresses the dynamic contact problem between a thermo‐electro‐viscoelastic body and a rigid foundation. The contact is bilateral, with friction modeled by Tresca's friction law. The weak formulation of the model is established as a coupled system consisting of a second‐order variational evolution inequality, a parabolic variational equation, and an elliptic variational equation. We prove the existence and uniqueness of a weak solution to this problem by applying the Banach fixed‐point theorem. Finally, we analyze a fully discrete scheme based on the Euler method and the finite element method, and we derive error estimates for the approximate solutions.