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In this work, we study a new thermoelastic model with two temperatures from the numerical point of view. The problem is written as a coupled linear system whose unknowns are the displacement field and the conductivity and thermodynamic temperatures. An existence and uniqueness result recently proved is recalled. Then, a fully discrete approximation is introduced by using the finite element method and the classical implicit Euler scheme. A main a priori error estimates result is proved and, under some appropriate regularity conditions on the continuous solution, we obtain the linear convergence. Finally, some numerical simulations are presented to demonstrate the numerical convergence and the discrete energy decay.

A Fully Discrete Approximation of a New Two-Temperature Thermoelastic Model