A simplified a posteriori error analysis of a second-order difference scheme for a singularly perturbed convection-diffusion problem

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-04-18 DOI:10.1007/s10910-025-01729-6

Jian Huang, Zhongdi Cen, Aimin Xu

引用次数: 0

Abstract

In this paper a numerical method on a posteriori mesh is presented to solve a second-order singularly perturbed convection-diffusion equation. A second-order three-point difference method is used to discretize the singularly perturbed convection-diffusion equation. A posteriori error analysis involving simple calculations with fewer proof techniques is developed for the second-order three-point difference method on an arbitrary mesh. A solution-adaptive algorithm based on a posteriori error analysis is designed to generate a posteriori mesh and the approximation solution. Numerical experiments verify the second-order uniform convergence of this method.

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奇异摄动对流扩散问题二阶差分格式的简化后验误差分析

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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

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.