Numerical analysis of a thermoelastic problem of Moore-Gibson-Thompson type with history dependence in the thermal displacement

被引：0

作者：

Bazarra, N. ^{[1
]}

Fernandez, J. R. ^{[1
]}

Quintanilla, R. ^{[2
]}

机构：

[1] Univ Vigo, Dept Matemat Aplicada 1, Escola Enxeneria Telecomunicac, Campus Lagoas Marcosende s-n, Vigo 36310, Spain

[2] UPC, Dept Matemat, ESEIAAT, Colom 11, Terrassa 08222, Barcelona, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 457卷

关键词：

Thermoelasticity of Moore-Gibson-Thompson type; History of finite time; Finite elements; Discrete stability; A priori error estimates; Numerical simulations;

D O I：

10.1016/j.cam.2024.116317

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we study, from the numerical point of view, a heat conduction model which is described by the history dependent version of the Moore-Gibson-Thompson equation. First, we consider the thermal problem, introducing a fully discrete approximation by means of the finite element method and the implicit Euler scheme. The discrete stability of its solution is proved, and an a priori error analysis is provided, which leads to the linear convergence imposing suitable regularity conditions. Secondly, we deal with the natural extension to the thermoelastic case. Following the analysis of the thermal problem, similar results are shown. Finally, we present some one-dimensional numerical simulations for both problems which demonstrate the accuracy of the approximations and the behavior of the discrete energies and the solutions.

引用

页数：15