非局部边界条件下椭圆型问题的数值解

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Electronic Transactions on Numerical Analysis Pub Date : 2023-01-01 DOI:10.1553/etna_vol59s179

Zorica Milovanović Jeknić, Bratislav Sredojević, Dejan Bojović

{"title":"非局部边界条件下椭圆型问题的数值解","authors":"Zorica Milovanović Jeknić, Bratislav Sredojević, Dejan Bojović","doi":"10.1553/etna_vol59s179","DOIUrl":null,"url":null,"abstract":"In this paper we consider a class of non-standard elliptic transmission problems in disjoint domains. As a model example, we consider an area consisting of two non-adjacent rectangles. In each subarea, a boundary-value problem of elliptic type is considered, where the interaction between their solutions is described by nonlocal integral conjugation conditions. An a priori estimate for its weak solution in an appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data, up to a slowly increasing logarithmic factor of the mesh size, is obtained.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the numerical solution of an elliptic problem with nonlocal boundary conditions\",\"authors\":\"Zorica Milovanović Jeknić, Bratislav Sredojević, Dejan Bojović\",\"doi\":\"10.1553/etna_vol59s179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider a class of non-standard elliptic transmission problems in disjoint domains. As a model example, we consider an area consisting of two non-adjacent rectangles. In each subarea, a boundary-value problem of elliptic type is considered, where the interaction between their solutions is described by nonlocal integral conjugation conditions. An a priori estimate for its weak solution in an appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data, up to a slowly increasing logarithmic factor of the mesh size, is obtained.\",\"PeriodicalId\":50536,\"journal\":{\"name\":\"Electronic Transactions on Numerical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Transactions on Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1553/etna_vol59s179\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Transactions on Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1553/etna_vol59s179","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了不相交域上的一类非标准椭圆传输问题。作为一个模型例子，我们考虑一个由两个不相邻矩形组成的区域。在每个子区域中，考虑一个椭圆型边值问题，其解之间的相互作用用非局部积分共轭条件来描述。证明了其弱解在适当的类sobolev空间中的先验估计。提出并分析了近似于该问题的有限差分格式。估计的收敛速度，兼容的平滑输入数据，直到一个缓慢增加的对数因子的网格大小，得到。

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

On the numerical solution of an elliptic problem with nonlocal boundary conditions

In this paper we consider a class of non-standard elliptic transmission problems in disjoint domains. As a model example, we consider an area consisting of two non-adjacent rectangles. In each subarea, a boundary-value problem of elliptic type is considered, where the interaction between their solutions is described by nonlocal integral conjugation conditions. An a priori estimate for its weak solution in an appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data, up to a slowly increasing logarithmic factor of the mesh size, is obtained.

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

Electronic Transactions on Numerical Analysis 数学-应用数学

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM).