An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

Abstract

In this paper we deal with the numerical analysis of the Lord-Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error J. Baldonedo acknowledges the funding by Xunta de Galicia (Spain) under the program Axudasá etapa predoutoral with Ref.

Inhomogeneous waves propagation in double-porosity thermoelastic media

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Polynomial stability for Lord–Shulman porous elasticity with microtemperature and strong time delay

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Thermo-poroelastic AVO modeling of Olkaria geothermal reservoirs

“…The LS theory has been extended to the porous case (i.e., the so-called thermo-poroelasticity) by incorporating Biot poroelasticity to couple elastic deformations with temperature (Noda, 1990;Nield and Bejan, 2006;Sharma, 2008;Carcione et al, 2019;Baldonedo et al, 2020). The theory predicts the presence of both Biot and thermal slow P waves besides the classical P and S waves.…”