Optimal Convergence of Thermoelastic Contact Problem Involving Nonlinear Hencky-Type Materials with Friction Conditions

We study the linear finite element approximation of thermoelastic frictional contact problem. The unilateral contact condition is weakly imposed by the penalty method. Our analysis yields error estimates that are contingent upon the penalty parameter epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} and the mesh size h. Furthermore, provided the solution maintains regularity, we establish a convergence result.