In this paper, we consider a one-dimensional thermoelastic Timoshenko system where the thermal coupling is acting on both the shear force and the bending moment, and the heat flux is given by Cattaneo’s law. Our contribution will consist in studying the numerical stability of a Timoshenko system with Cattaneo’s law. We introduce a \(P_{1}\) finite element method for space discretization and implicit Euler scheme for time discretization. Then we prove that the associated discrete energy decreases and we establish a priori error estimates. Finally, we obtain some numerical simulations.

中文翻译：

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基于 Cattaneo 定律的 Timoshenko 系统的离散能量行为

在本文中，我们考虑一维热弹性 Timoshenko 系统，其中热耦合作用于剪切力和弯矩，并且热通量由 Cattaneo 定律给出。我们的贡献将包括利用 Cattaneo 定律研究 Timoshenko 系统的数值稳定性。我们引入了空间离散化的\(P_{1}\)有限元方法和时间离散化的隐式欧拉方案。然后我们证明相关的离散能量减少，并建立先验误差估计。最后，我们获得了一些数值模拟结果。