Finite Element Approximation of a Hemivariational Inequality for Steady-State Heat Conduction: Double-Limit Convergence of Penalization and Discretization

In this paper we study the numerical approximation and convergence analysis of a steady-state heat conduction problem with mixed boundary conditions. The physical model is governed by a hemivariational inequality depending on a heat transfer parameter $α> 0$. We consider the finite element approxima