{"title":"A decoupled nonconforming finite element method for biharmonic equation in three dimensions","authors":"Xuewei Cui, Xuehai Huang","doi":"10.1016/j.apnum.2025.02.012","DOIUrl":null,"url":null,"abstract":"<div><div>This study focuses on a low-order decoupled nonconforming finite element method for solving the three-dimensional biharmonic equation. The main contribution is to discretize the generalized Stokes equation using a low-order nonconforming element for the <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> space and the lowest order edge element for the pressure. Additionally, the method employs the Lagrange element to solve the Poisson equations. To validate the theoretical convergence rates, numerical experiments are conducted.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 300-311"},"PeriodicalIF":2.4000,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927425000364","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
This study focuses on a low-order decoupled nonconforming finite element method for solving the three-dimensional biharmonic equation. The main contribution is to discretize the generalized Stokes equation using a low-order nonconforming element for the space and the lowest order edge element for the pressure. Additionally, the method employs the Lagrange element to solve the Poisson equations. To validate the theoretical convergence rates, numerical experiments are conducted.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
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(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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