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Fully discrete approximations and an a priori error analysis of a two-temperature thermo-elastic model with microtemperatures

Baldonedo Jacobo, Fernández José R., Quintanilla Ramón

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 1

93--103

In this paper, we consider, from a numerical point of view, a two-temperature poro-thermoelastic problem. The model is written as a coupled linear system of hyperbolic and elliptic partial differential equations. An existence result is proved and energy decay properties are recalled. Then we introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained, from which the linear convergence of the approximation is deduced under an appropriate additional regularity. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation, the decay of the discrete energy and the behaviour of the solution depending on a constitutive parameter.

On the fully discrete approximations of the MGT two-temperatures thermoelastic problem

Baldonedo J., Fernández J. R., Quintanilla R.

Archives of Mechanics

2022

Vol. 74, nr 5

391--407

We consider a one-dimensional two-temperatures thermoelastic model. The corresponding variational problem leads to a coupled system which is written in terms of the mechanical velocity, the temperature speed and the inductive temperature. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are proved and the linear convergence of the approximations is deduced under suitable additional regularity conditions. Finally, some numerical simulations are shown to demonstrate the accuracy of the proposed algorithm and the behavior of the discrete energy.