Computational analysis demonstrates linear convergence in porous thermoelastic models with microtemperatures, highlighting stable prediction of coupled thermal memory systems.
In this work, we study, from the numerical point of view, a porous thermoelastic problem with microtemperatures, where the thermal evolution is influenced by the history of both the temperature and microtemperatures. This leads to a coupled system of partial integro‐differential equations. Then, fully discrete approximations are provided by using the implicit Euler scheme and the finite element method. Some numerical issues, such as the discrete stability and an a priori error analysis, are discussed, and the linear convergence of the approximations is concluded for a suitable additional regularity. Finally, we present some one‐dimensional numerical examples to show the numerical convergence and the behavior of the discrete energy.
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Bazarra et al. (2026) studied this question.
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