Numerical Approximation of the Timoshenko System with Temperature and Microtemperature Effects in the Absence of Thermal Conductivity

Abstract

This study presents a numerical investigation of a thermoelastic Timoshenko system where dissipation arises exclusively from microtemperature effects, with thermal diffusion neglected. The primary objective is to analyze the system’s energy evolution and exponential decay properties. We start by formulating the problem variationally, employing transformed derivatives to derive a coupled system of four first-order variational equations. A fully discrete numerical scheme is then proposed, and its discrete stability is rigorously established. We also derive a priori error estimates for the method. To support our theoretical analysis, numerical experiments are carried out, confirming the expected decay behavior and accuracy of the solution.