{"title":"三维双调和方程的解耦非协调有限元法","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":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"2025-06-01\",\"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\":\"2025/2/19 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","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":"2025/2/19 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A decoupled nonconforming finite element method for biharmonic equation in three dimensions
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:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
