NUMERICAL ANALYSIS OF THE PENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH TRESCA’S FRICTION IN THERMO-ELECTRO-VISCO-ELASTICITY

We consider the penalty method applied to contact problem in thermo-electro- visco-elasticity with the Signorini’s condition and Tresca’s friction law. Mathematical prop- erties, such as the existence of a solution to the penalty problem and its convergence to the solution of the original problem, are reported. We then study two numerical approximation schemes of penalized problem, a spatially semi-discrete scheme and a fully discrete approx- imation by using the forward Euler scheme with the finite element method and prove its convergence. Finally, we propose an iterative method to solve the resulting finite element system and establish its convergence.