<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>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 <italic>a priori </italic>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.</p>
</abstract>

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.

Fully Discrete Approximations and an <italic>a Priori</italic> Error Analysis of a Two–Temperature Thermo–Elastic Model with Microtemperatures

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fully Discrete Approximations and an  Error Analysis of a Two–Temperature Thermo–Elastic Model with Microtemperatures

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...

Fully Discrete Approximations and an a Priori Error Analysis of a Two–Temperature Thermo–Elastic Model with Microtemperatures

Published Online: Mar 26, 2024

Page range: 93 - 103

Received: Mar 30, 2023

Accepted: Oct 02, 2023

DOI: https://doi.org/10.61822/amcs-2024-0007

Keywords
two temperatures, poro-thermoelasticity, microtemperatures, finite elements, error estimates

© 2024 Jacobo Baldonedo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fully Discrete Approximations and an a Priori Error Analysis of a Two–Temperature Thermo–Elastic Model with Microtemperatures

Published Online: Mar 26, 2024

Page range: 93 - 103

Received: Mar 30, 2023

Accepted: Oct 02, 2023

DOI: https://doi.org/10.61822/amcs-2024-0007

Keywordstwo temperatures, poro-thermoelasticity, microtemperatures, finite elements, error estimates

© 2024 Jacobo Baldonedo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
two temperatures, poro-thermoelasticity, microtemperatures, finite elements, error estimates