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 analysis is provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation, the comparison with the classical Fourier theory and the behavior of the solution in two-dimensional examples.

中文翻译：

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具有微观温度的 Lord-Shulman 多孔热弹性问题的先验误差分析

在本文中，我们处理具有孔隙度和微观温度的 Lord-Shulman 热弹性问题的数值分析。热机械问题导致耦合系统由线性双曲偏微分方程组成，这些方程根据位移场和体积分数、温度和微观温度的变换而写成。陈述存在性和唯一性结果。然后，使用有限元方法和隐式欧拉方案引入了完全离散的近似。显示了离散稳定性属性，并提供了先验误差分析，从中可以在合适的规律性条件下导出线性收敛。最后，给出了一些数值模拟来证明近似的准确性，