Maximum-Norm a Posteriori Error Bounds for an Extrapolated Upwind Scheme Applied to a Singularly Perturbed Convection-Diffusion Problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-19 DOI:10.1007/s00009-024-02698-x

Torsten Linß, Goran Radojev

引用次数: 0

Abstract

Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for the proposed method on arbitrary meshes. It is shown that the resulting error estimator can be used to steer an adaptive mesh algorithm that generates meshes resolving layers and singularities. Numerical results are presented that illustrate the theoretical findings.

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应用于奇异扰动对流扩散问题的外推上风方案的最大正态后验误差边界

理查德森外推法被应用于一个简单的一阶上风差分方案，用于逼近一维奇异扰动对流扩散问题的解。在任意网格上，为所提出的方法导出了稳健的后验误差边界。结果表明，由此得出的误差估计值可用于指导自适应网格算法，生成解决层和奇异性的网格。文中给出的数值结果说明了理论发现。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.