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Quasistatic Porous-Thermoelastic Problems: An a Priori Error Analysis

Author

Listed:
  • Jacobo Baldonedo

    (CINCTEX, Departamento de Ingeniería Mecánica, Universidade de Vigo, Máquinas y Motores Térmicos y Fluídos, 36310 Vigo, Spain)

  • José R. Fernández

    (Departamento de Matemática Aplicada I, Universidade de Vigo, 36310 Vigo, Spain)

  • José A. López-Campos

    (CINCTEX, Departamento de Ingeniería Mecánica, Universidade de Vigo, Máquinas y Motores Térmicos y Fluídos, 36310 Vigo, Spain)

Abstract

In this paper, we deal with the numerical approximation of some porous-thermoelastic problems. Since the inertial effects are assumed to be negligible, the resulting motion equations are quasistatic. Then, by using the finite element method and the implicit Euler scheme, a fully discrete approximation is introduced. We prove a discrete stability property and a main error estimates result, from which we conclude the linear convergence under appropriate regularity conditions on the continuous solution. Finally, several numerical simulations are shown to demonstrate the accuracy of the approximation, the behavior of the solution and the decay of the discrete energy.

Suggested Citation

  • Jacobo Baldonedo & José R. Fernández & José A. López-Campos, 2021. "Quasistatic Porous-Thermoelastic Problems: An a Priori Error Analysis," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1436-:d:578270
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    References listed on IDEAS

    as
    1. Fernández, J.R. & Masid, M., 2017. "A porous thermoelastic problem: An a priori error analysis and computational experiments," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 117-135.
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    1. Bazarra, N. & Fernández, J.R. & Quintanilla, R., 2020. "An a priori error analysis of poro-thermoviscoelastic problems," Applied Mathematics and Computation, Elsevier, vol. 379(C).

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