Coupled parabolic-hyperbolic system often appears in the studies of thermoelasticity, magnetoelasticity, biological problems and radiation hydrodynamics with high temperature. In this paper, we investigate a problem of thermal diffusion in elastic body with moving boundary. Three numerical methods, two uncoupled and one coupled, all with quadratic convergence order in time and space, are presented and compared in relation to the execution time. Tables and figures of the approximate solution are shown to verify the efficiency and feasibility of the proposed method. In addition, we show that the numerical results are consistent with the theoretical results. The approximate numerical solutions are calculated using the finite element method in spatial variable and finite difference method in time. To compare different numerical schemes, we show the convergence rates through numerical simulations with calculated error and the execution time.

中文翻译：

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具有移动边界的弹性体热扩散问题的数值方法

耦合抛物双曲线系统经常出现在高温热弹性、磁弹性、生物学问题和辐射流体力学的研究中。在本文中，我们研究了具有移动边界的弹性体中的热扩散问题。三种数值方法，两种非耦合方法和一种耦合方法，在时间和空间上均具有二次收敛阶次，并在执行时间方面进行了比较。给出了近似解的表格和图形，以验证所提出方法的有效性和可行性。此外，我们表明数值结果与理论结果一致。近似数值解采用空间变量有限元法和时间有限差分法计算。为了比较不同的数值方案，