In this work, we study a thermoelastic Bresse system from both mathematical and numerical points of view. The dual-phase-lag heat conduction theory is used to model the heat transfer. An existence and uniqueness result is obtained by using the theory of linear semigroups. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are shown, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behavior of the solution with respect to a constitutive parameter.

在这项工作中，我们从数学和数值的角度研究了一种热弹性的Bresse系统。采用双相滞后热传导理论对传热进行建模。利用线性半群理论获得了存在性和唯一性结果。然后，通过使用有限元方法和隐式Euler方案引入完全离散的近似值。显示了先验误差估计，在适当的规律性条件下，可以从中得出线性收敛。最后，提出了一些数值模拟，以证明近似值的精确度以及关于本构参数的解的行为。