An a priori error analysis of a thermoelastic problem with history dependence on the mechanical and thermal components

Abstract

Here, we provide an a priori error analysis of a thermoelastic problem, with the Moore–Gibson–Thompson (MGT) equation, where the history dependence is assumed on both the mechanical and thermal parts. An existence and uniqueness result, and the exponential stability, are recalled. Then, a fully discrete approximation is introduced by using the finite element method and the implicit Euler scheme, to approximate the spatial variable and the time derivatives, respectively. A discrete stability property is proved and a main a priori error estimates result is obtained. The linear convergence of the approximations is deduced under suitable regularity conditions. Finally, we perform some one- and two-dimensional simulations to show the accuracy of the algorithm, the exponential decay of the discrete energy and the behavior of the solution.

This paper is part of the project “Qualitative and numerical analyses of some thermomechanical problems (ACUANUTER)” (Ref. PID2024-156827NB-I00), which is currently under evaluation by the Spanish Ministry of Science, Innovation and Universities

Peer Reviewed

Postprint (published version)