通量先验估计的存在性与高变系数扩散方程迭代方法收敛性之间的联系

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-06-01 DOI:10.1515/rnam-2022-0012

G. Kobelkov, E. Schnack

{"title":"通量先验估计的存在性与高变系数扩散方程迭代方法收敛性之间的联系","authors":"G. Kobelkov, E. Schnack","doi":"10.1515/rnam-2022-0012","DOIUrl":null,"url":null,"abstract":"Abstract An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients\",\"authors\":\"G. Kobelkov, E. Schnack\",\"doi\":\"10.1515/rnam-2022-0012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.\",\"PeriodicalId\":49585,\"journal\":{\"name\":\"Russian Journal of Numerical Analysis and Mathematical Modelling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Numerical Analysis and Mathematical Modelling\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/rnam-2022-0012\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Numerical Analysis and Mathematical Modelling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/rnam-2022-0012","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

摘要针对高变系数扩散方程的边值问题，提出了一种迭代次数与系数跳跃无关的迭代方法。该方法在迭代的每一步应用泊松方程的一个解。在本文中，我们扩展了迭代方法所适用的一类域。

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

Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients

Abstract An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.

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

Russian Journal of Numerical Analysis and Mathematical Modelling 数学-工程：综合

CiteScore

1.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest. Topics: -numerical analysis- numerical linear algebra- finite element methods for PDEs- iterative methods- Monte-Carlo methods- mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.