Abstract

In this work, we study an approximate problem arising in the incremental thermoelasticity. The existence of a unique solution is proved applying the theory of linear semigroups. The exponential energy decay is also considered. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown. Finally, numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the model. In view of our numerical results the approximate problem could be used only when a certain parameter is small if we compare it with other parameters arising in the problem.

摘要

在这项工作中，我们研究了增量热弹性中产生的一个近似问题。应用线性半群理论证明了唯一解的存在。还考虑了指数能量衰减。然后，使用有限元方法和隐式Euler方案引入完全离散的近似值。显示了离散的稳定性和先验误差估计。最后，通过数值模拟证明了逼近的准确性和模型的行为。根据我们的数值结果，如果将某个参数与问题中出现的其他参数进行比较，则仅当某个参数较小时才可以使用近似问题。