扩散-平流-反应问题的保守网络元法

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-05-05 DOI:10.1051/m2an/2023040

J. Coatléven

{"title":"扩散-平流-反应问题的保守网络元法","authors":"J. Coatléven","doi":"10.1051/m2an/2023040","DOIUrl":null,"url":null,"abstract":"We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A conservative network element method for diffusion-advection-reaction problems\",\"authors\":\"J. Coatléven\",\"doi\":\"10.1051/m2an/2023040\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.\",\"PeriodicalId\":50499,\"journal\":{\"name\":\"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/m2an/2023040\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2023040","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

通过对非保守网络元法的修正，导出了非保守网络元法求解非均质和各向异性扩散问题的保守网络元法，并将其推广到一个附加平流项的近似。数值格式具有令人联想到经典有限体积法的通量公式。其收敛性自然受到网络要素理论的支配。数值结果表明，该方法即使在变形点云上也具有良好的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A conservative network element method for diffusion-advection-reaction problems

We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.