格罗斯-皮塔耶夫斯基特征值问题的混合有限元:先验误差分析和有保证的能量下限

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED
Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim
{"title":"格罗斯-皮塔耶夫斯基特征值问题的混合有限元:先验误差分析和有保证的能量下限","authors":"Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim","doi":"10.1093/imanum/drae048","DOIUrl":null,"url":null,"abstract":"We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound\",\"authors\":\"Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim\",\"doi\":\"10.1093/imanum/drae048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.\",\"PeriodicalId\":56295,\"journal\":{\"name\":\"IMA Journal of Numerical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IMA Journal of Numerical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imanum/drae048\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imanum/drae048","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

我们为非线性 Gross-Pitaevskii 特征值问题的最低阶 Raviart-Thomas 有限元离散化建立了先验误差分析。对于主变量和对偶变量,以及特征值和能量近似,都获得了最佳收敛率。与自然意味着能量上限的符合方法不同,所提出的混合离散化为基态能量提供了有保证的渐进精确下限。一系列数值实验对理论结果进行了说明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound
We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.
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
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis 数学-应用数学
CiteScore
5.30
自引率
4.80%
发文量
79
审稿时长
6-12 weeks
期刊介绍: The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信