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Numerical analysis of a type III thermo-porous-elastic problem with microtemperatures
Computational and Applied Mathematics ( IF 2.998 ) Pub Date : 2020-08-11 , DOI: 10.1007/s40314-020-01248-x
Noelia Bazarra , José R. Fernández , Ramón Quintanilla

In this work, we consider, from the numerical point of view, a poro-thermoelastic problem. The thermal law is the so-called of type III and the microtemperatures are also included into the model. The variational formulation of the problem is written as a linear system of coupled first-order variational equations. Then, fully discrete approximations are introduced by using the classical finite-element method and the implicit Euler scheme. A discrete stability property and an a priori error estimates result are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some one- and two-dimensional numerical simulations are presented to show the accuracy of the approximation and the behavior of the solution.

中文翻译:

含微温度的III型热多孔弹性问题的数值分析

在这项工作中,我们从数值的角度考虑了一个孔隙热弹性问题。热定律是所谓的III型,并且微观温度也包括在模型中。问题的变分形式写为耦合的一阶变分方程的线性系统。然后,使用经典的有限元方法和隐式Euler格式引入完全离散的近似值。证明了离散的稳定性和先验误差估计结果,从中可以得出在合适的附加规则性条件下算法的线性收敛性。最后,提出了一些一维和二维数值模拟,以显示逼近的准确性和解的性质。
更新日期:2020-08-11
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