A Moore‐Gibson‐Thompson heat conduction equation for non centrosymmetric rigid solids

Abstract

In this paper, we propose a new thermal model based on the so‐called Moore‐Gibson‐Thompson equation for heat conduction, assuming that the material is not centrosymmetric. The existence of a unique solution is proved, although only the main steps of its proof are provided for the sake of simplicity in the presentation. A sufficient condition is proposed to guarantee the stability of the solutions. Then, a fully discrete scheme is introduced by using the classical finite element scheme and the implicit Euler scheme. A discrete stability property and an a priori error analysis are shown, from which the linear convergence of the approximations is deduced. Finally, some numerical simulations in one‐dimensional examples are performed to show the behavior of the discrete energy decay.