双谐波特征值问题的混合非连续伽勒金方法的多网格离散化

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-05 DOI:10.1002/mma.10455

Jinhua Feng, Shixi Wang, Hai Bi, Yidu Yang

{"title":"双谐波特征值问题的混合非连续伽勒金方法的多网格离散化","authors":"Jinhua Feng, Shixi Wang, Hai Bi, Yidu Yang","doi":"10.1002/mma.10455","DOIUrl":null,"url":null,"abstract":"<p>The Ciarlet–Raviart mixed method is popular for the biharmonic equations/eigenvalue problem. In this paper, we propose a multigrid discretization based on the shifted-inverse iteration of Ciarlet–Raviart mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. We prove the a priori error estimates of the approximate eigenpairs. We also give the a posteriori error estimates of the approximate eigenvalues and prove the reliability of the estimator and implement adaptive computation. Numerical experiments show that our method can efficiently compute biharmonic eigenvalues.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2635-2654"},"PeriodicalIF":2.1000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem\",\"authors\":\"Jinhua Feng, Shixi Wang, Hai Bi, Yidu Yang\",\"doi\":\"10.1002/mma.10455\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The Ciarlet–Raviart mixed method is popular for the biharmonic equations/eigenvalue problem. In this paper, we propose a multigrid discretization based on the shifted-inverse iteration of Ciarlet–Raviart mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. We prove the a priori error estimates of the approximate eigenpairs. We also give the a posteriori error estimates of the approximate eigenvalues and prove the reliability of the estimator and implement adaptive computation. Numerical experiments show that our method can efficiently compute biharmonic eigenvalues.</p>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 2\",\"pages\":\"2635-2654\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.10455\",\"RegionNum\":3,\"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":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10455","RegionNum":3,"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

Ciarlet-Raviart 混合法是双谐波方程/特征值问题的常用方法。本文针对双谐波特征值问题，提出了一种基于 Ciarlet-Raviart 混合非连续 Galerkin 方法移反迭代的多网格离散化方法。我们证明了近似特征对的先验误差估计。我们还给出了近似特征值的后验误差估计，证明了估计器的可靠性，并实现了自适应计算。数值实验表明，我们的方法可以高效地计算双谐波特征值。

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

The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem

The Ciarlet–Raviart mixed method is popular for the biharmonic equations/eigenvalue problem. In this paper, we propose a multigrid discretization based on the shifted-inverse iteration of Ciarlet–Raviart mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. We prove the a priori error estimates of the approximate eigenpairs. We also give the a posteriori error estimates of the approximate eigenvalues and prove the reliability of the estimator and implement adaptive computation. Numerical experiments show that our method can efficiently compute biharmonic eigenvalues.

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.