Penalization of a frictional thermoelastic contact problem with generalized temperature dependent conditions

We consider a convergence analysis of the penalty method applied to static thermo-elastic contact problem with generalized temperature dependent unilateral frictional contact conditions and a generalized Signorini's thermal contact condition. The friction is modeled with a temperature dependent variant of Coulomb's law and in both frictional and thermal contact conditions, the heat exchange effect is taking into account. We first consider our thermoelastic contact problem and under various assumptions, we establish its unique weak solvability. Then, after introducing the associated penalized problem and proving the existence of its solution, the weak convergence of the penalty solution to the solution of the initial problem, is carried out. Moreover, we provide the convergence of the discrete penalty solutions to the solution of the constrained initial problem as both the discretization and the penalty parameters approach zero.