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

IF 1.1 3区数学 Q1 MATHEMATICS Mediterranean Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1007/s00009-024-02698-x

Torsten Linß, Goran Radojev

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引用次数: 0

摘要

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。

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

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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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.