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A strain gradient problem with a fourth-order thermal law

Published: 09 July 2024 Publication History

Abstract

In this paper, a strain gradient thermoelastic problem is studied from the numerical point of view. The heat conduction is modeled by using the type II thermal law and the second gradient of the thermal displacement is also included in the set of independent constitutive variables. An existence and uniqueness result is recalled. Then, the fully discrete approximations are introduced by using the implicit Euler scheme and the finite element method. A discrete stability property and a main a priori error estimates results are proved. Then, some numerical simulations are performed, including some issues as the numerical convergence of the approximations, the effect of two possible dissipative terms (second- and fourth-order) or a comparison with the type II strain gradient thermoelasticity.

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Bazarra N., Fernández J.R., Muñoz-Rivera J.E., Ochoa E., Quintanilla R., A viscous strain gradient problem involving type II thermoelasticity, 2023, submitted for publication.

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Published In

cover image Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics  Volume 445, Issue C
Aug 2024
586 pages

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 09 July 2024

Author Tags

  1. Strain gradient thermoelasticity
  2. Fourth-order equations
  3. Dissipation mechanisms
  4. Finite elements
  5. a priori error estimates
  6. Numerical simulations

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