A poro-thermoelastic problem with dissipative heat conduction
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In this work, we study from the mathematical and numerical points of view a poro-thermoelastic problem. A long-term memory is assumed on the heat equation. Under some assumptions on the constitutive tensors, the resulting linear system is composed of hyperbolic partial differential equations with a dissipative mechanism in the temperature equation. An existence and uniqueness result is proved using the theory of contractive semigroups. Then, a fully discrete approximation is introduced applying the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is obtained. A priori error estimates are also shown, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, one- and two-numerical simulations are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.
CitationBazarra, N. [et al.]. A poro-thermoelastic problem with dissipative heat conduction. "Journal of thermal stresses", 18 Juliol 2020, vol. 43, num. 11, p. 1415-1436.