Analysis of a Moore–Gibson–Thompson thermoelastic problem

In this work, we numerically consider a thermoelastic problem where the thermal law is modeled using so-called Moore–Gibson–Thompson equation. This thermomechanical written as coupled system composed of hyperbolic partial differential equation for transformation displacement field and parabolic temperature. Its variational formulation in terms derivatives above transformed functions, leading to linear made two first-order equations. Then, fully discrete algorithm introduced stability property proved. A priori error estimates are also provided, from which convergence derived under suitable regularity conditions. Finally, some numerical results shown, including approximations, comparisons with Lord–Shulman type III Green–Naghdi theories, two-dimensional examples demonstrate behavior solution. • studied. implemented. An analysis performed. The simulations compared other theories.