A porous thermoelastic problem with microtemperatures

ABSTRACT

In this article, we consider from the numerical point of view a thermodynamical problem involving a linear elastic material with inner structure, whose particles in addition to the classical displacement possess microtemperatures. The variational formulation of this problem is written as a system of coupled linear parabolic variational equations in terms of velocity, porosity speed, microtemperatures, and temperature. Then, fully discrete approximations are introduced using the finite element method and the backward Euler scheme. A stability property is proved and some a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the solution.

KEYWORDS:

• Error estimates
• finite elements
• microtemperatures
• numerical simulations
• thermoporoelasticity

Acknowledgments

We would like to thank the anonymous referee for the careful and thorough review of the article, which improved the conditions to obtain the results.