Unconditionally Energy Stable and First-Order Accurate Numerical Schemes for the Heat Equation with Uncertain Temperature-Dependent Conductivity

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI:10.4208/ijnam2023-1035

Fiordilino, J. A., Winger, M.

引用次数: 1

Abstract

In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving computational efficiency. Both mixed and Robin-type boundary conditions are treated. In contrast with alternative, related methodologies, stability and convergence are unconditional. In particular, we prove unconditional, energy stability and optimal-order error estimates. A battery of numerical tests are presented to illustrate both the theory and application of these algorithms.

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具有不确定温度相关电导率的热方程的无条件能量稳定和一阶精确数值格式

本文给出了具有不确定温度相关导热系数的热方程的一阶精确数值解法。每个算法为集合集生成一个共享系数矩阵，提高了计算效率。对混合边界条件和罗宾型边界条件进行了处理。与其他相关方法相比，稳定性和收敛性是无条件的。特别地，我们证明了无条件、能量稳定性和最优阶误差估计。通过一系列的数值试验来说明这些算法的理论和应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.