非中心对称刚性固体的Moore - Gibson - Thompson热传导方程

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED
Noelia Bazarra, José R. Fernández, Ramón Quintanilla
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引用次数: 0

摘要

在本文中,我们提出了一种新的基于Moore - Gibson - Thompson热传导方程的热模型,假设材料不是中心对称的。本文证明了一个唯一解的存在性,但为了简单起见,只给出了证明的主要步骤。给出了保证解稳定的充分条件。然后,利用经典有限元格式和隐式欧拉格式引入了全离散格式。给出了离散稳定性的性质和先验误差分析,并由此导出了近似的线性收敛性。最后,对一维例子进行了数值模拟,以显示离散能量衰减的行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Moore‐Gibson‐Thompson heat conduction equation for non centrosymmetric rigid solids
Abstract In this paper, we propose a new thermal model based on the so‐called Moore‐Gibson‐Thompson equation for heat conduction, assuming that the material is not centrosymmetric. The existence of a unique solution is proved, although only the main steps of its proof are provided for the sake of simplicity in the presentation. A sufficient condition is proposed to guarantee the stability of the solutions. Then, a fully discrete scheme is introduced by using the classical finite element scheme and the implicit Euler scheme. A discrete stability property and an a priori error analysis are shown, from which the linear convergence of the approximations is deduced. Finally, some numerical simulations in one‐dimensional examples are performed to show the behavior of the discrete energy decay.
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来源期刊
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
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