A dual-phase-lag porous-thermoelastic problem with microtemperatures

N. Bazarra; J. R. Fernández; R. Quintanilla; N. Bazarra; J. R. Fernández; R. Quintanilla

doi:10.3934/era.2022065

Electronic Research Archive

2022, Volume 30, Issue 4: 1236-1262. doi: 10.3934/era.2022065

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Research article

A dual-phase-lag porous-thermoelastic problem with microtemperatures

1.
Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
2.
Departamento de Matemáticas, E.S.E.I.A.A.T.-U.P.C., Colom 11, 08222 Terrassa, Barcelona, Spain

Received: 21 September 2021 Revised: 10 December 2021 Accepted: 16 December 2021 Published: 15 March 2022

In this work, we consider a multi-dimensional dual-phase-lag problem arising in porous-thermoelasticity with microtemperatures. An existence and uniqueness result is proved by applying the semigroup of linear operators theory. Then, by using the finite element method and the Euler scheme, a fully discrete approximation is numerically studied, proving a discrete stability property and a priori error estimates. Finally, we perform some numerical simulations to demonstrate the accuracy of the approximation and the behavior of the solution in one- and two-dimensional problems.
- dual-phase-lag,
- porous-thermoelasticity with microtemperatures,
- existence and uniqueness,
- finite elements,
- a priori error estimates,
- numerical simulations
Citation: N. Bazarra, J. R. Fernández, R. Quintanilla. A dual-phase-lag porous-thermoelastic problem with microtemperatures[J]. Electronic Research Archive, 2022, 30(4): 1236-1262. doi: 10.3934/era.2022065

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Abstract

In this work, we consider a multi-dimensional dual-phase-lag problem arising in porous-thermoelasticity with microtemperatures. An existence and uniqueness result is proved by applying the semigroup of linear operators theory. Then, by using the finite element method and the Euler scheme, a fully discrete approximation is numerically studied, proving a discrete stability property and a priori error estimates. Finally, we perform some numerical simulations to demonstrate the accuracy of the approximation and the behavior of the solution in one- and two-dimensional problems.

References

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