三维有限元的局部逐点收敛性

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2023-06-23 DOI:10.1007/s11766-023-3911-9

Jing-hong Liu, Qi-ding Zhu

{"title":"三维有限元的局部逐点收敛性","authors":"Jing-hong Liu, Qi-ding Zhu","doi":"10.1007/s11766-023-3911-9","DOIUrl":null,"url":null,"abstract":"<div>For an elliptic problem with variable coefficients in three dimensions, this article discusses local pointwise convergence of the three-dimensional (3D) finite element. First, the Green’s function and the derivative Green’s function are introduced. Secondly, some relationship of norms such as L2-norms, W1,∞-norms, and negative-norms in locally smooth subsets of the domain Ω is derived. Finally, local pointwise convergence properties of the finite element approximation are obtained.</div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"38 2","pages":"210 - 222"},"PeriodicalIF":1.0000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11766-023-3911-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Local pointwise convergence of the 3D finite element\",\"authors\":\"Jing-hong Liu, Qi-ding Zhu\",\"doi\":\"10.1007/s11766-023-3911-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>For an elliptic problem with variable coefficients in three dimensions, this article discusses local pointwise convergence of the three-dimensional (3D) finite element. First, the Green’s function and the derivative Green’s function are introduced. Secondly, some relationship of norms such as L2-norms, W1,∞-norms, and negative-norms in locally smooth subsets of the domain Ω is derived. Finally, local pointwise convergence properties of the finite element approximation are obtained.</div>\",\"PeriodicalId\":55568,\"journal\":{\"name\":\"Applied Mathematics-A Journal of Chinese Universities Series B\",\"volume\":\"38 2\",\"pages\":\"210 - 222\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11766-023-3911-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics-A Journal of Chinese Universities Series B\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11766-023-3911-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-023-3911-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

对于三维变系数椭圆型问题，讨论了三维有限元的局部点向收敛性。首先，介绍了格林函数及其导数。其次，导出了域Ω的局部光滑子集上l2 -范数、W1、∞-范数和负范数之间的关系。最后，给出了有限元逼近的局部点向收敛性。

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

Local pointwise convergence of the 3D finite element

For an elliptic problem with variable coefficients in three dimensions, this article discusses local pointwise convergence of the three-dimensional (3D) finite element. First, the Green’s function and the derivative Green’s function are introduced. Secondly, some relationship of norms such as L²-norms, W^1,∞-norms, and negative-norms in locally smooth subsets of the domain Ω is derived. Finally, local pointwise convergence properties of the finite element approximation are 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

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.