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Numerical Analysis of a Swelling Poro-Thermoelastic Problem with Second Sound

Author

Listed:
  • Noelia Bazarra

    (Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain)

  • José R. Fernández

    (Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain)

  • María Rodríguez-Damián

    (Departamento de Informática, Universidade de Vigo, Escola de Enxeñería Industrial, 36310 Vigo, Spain)

Abstract

In this paper, we analyze, from the numerical point of view, a swelling porous thermo-elastic problem. The so-called second-sound effect is introduced and modeled by using the simplest Maxwell–Cattaneo law. This problem leads to a coupled system which is written by using the displacements of the fluid and the solid, the temperature and the heat flux. The numerical analysis of this problem is performed applying the classical finite element method with linear elements for the spatial approximation and the backward Euler scheme for the discretization of the time derivatives. Then, we prove the stability of the discrete solutions and we provide an a priori error analysis. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximations, the exponential decay of the discrete energy and the dependence on a coupling parameter.

Suggested Citation

  • Noelia Bazarra & José R. Fernández & María Rodríguez-Damián, 2023. "Numerical Analysis of a Swelling Poro-Thermoelastic Problem with Second Sound," Mathematics, MDPI, vol. 11(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1456-:d:1099825
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