VEM discretization allowing small edges for the reaction-convection-diffusion equation: source and spectral problems

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-09-05 DOI:10.1051/m2an/2023069

Felipe Lepe, Gonzalo Rivera

引用次数: 0

Abstract

In this paper we analyze a lowest order virtual element method for the classic load reaction-convection-diffusion problem and the convection-diffusion spectral problem, where the assumptions on the polygonal meshes allow to consider small edges for the polygons. Under well defined seminorms depending on a suitable stabilization for this geometrical approach, we derive the well posedness of the numerical scheme and error estimates for the load problem, whereas for the spectral problem we derive convergence and error estimates fo the eigenvalues and eigenfunctions. We report numerical tests to asses the performance of the small edges on our numerical method for both problems under consideration.

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允许小边缘反应-对流-扩散方程的VEM离散化:源和光谱问题

本文分析了经典荷载-反应-对流-扩散问题和对流-扩散谱问题的最低阶虚元法，其中多边形网格的假设允许考虑多边形的小边。在定义良好的半模下，根据该几何方法的适当稳定性，我们导出了负载问题的数值格式的适定性和误差估计，而对于谱问题，我们导出了特征值和特征函数的收敛性和误差估计。我们报告了数值测试，以评估我们的数值方法对这两个问题的小边的性能。

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

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.