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  4. A numerical study of swelling porous thermoelastic media with second sound

A numerical study of swelling porous thermoelastic media with second sound

MMC.
2023;
Volume 10, Number 3
: pp. 772–783
https://doi.org/10.23939/mmc2023.03.772
Received: February 18, 2023
Revised: July 10, 2023
Accepted: July 18, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 772–783 (2023)

Authors:
  1. A. Smouk
  2. A. Radid
  3. A. Soufyane
1
Department of Mathematics and Informatics, Hassan II University, FSAC, Fundamental and Applied Mathematics Laboratory, Casablanca, Morocco
2
Department of Mathematics and Informatics, Hassan II University, FSAC, Fundamental and Applied Mathematics Laboratory, Casablanca, Morocco
3
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates

In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law.  We study the numerical energy and the exponential decay of the thermoelastic problem.  First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations.  A fully discrete algorithm is introduced and a discrete stability property is proven.  A priori error estimates are also provided.  Finally, some numerical results are given to demonstrate the behavior of the solution.

swelling porous
second sound
exponential stability
finite elements
numerical energy
numerical results
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