Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu
{"title":"三维Alfeld分裂上的离散弹性复合体","authors":"Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu","doi":"10.1007/s00211-023-01381-9","DOIUrl":null,"url":null,"abstract":"<p>We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that derives the elasticity complex from de Rham complexes, and smoother finite element differential forms.\n</p>","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":"1 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"A discrete elasticity complex on three-dimensional Alfeld splits\",\"authors\":\"Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu\",\"doi\":\"10.1007/s00211-023-01381-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that derives the elasticity complex from de Rham complexes, and smoother finite element differential forms.\\n</p>\",\"PeriodicalId\":49733,\"journal\":{\"name\":\"Numerische Mathematik\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2023-11-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerische Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00211-023-01381-9\",\"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":"Numerische Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00211-023-01381-9","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A discrete elasticity complex on three-dimensional Alfeld splits
We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that derives the elasticity complex from de Rham complexes, and smoother finite element differential forms.
期刊介绍：
Numerische Mathematik publishes papers of the very highest quality presenting significantly new and important developments in all areas of Numerical Analysis. "Numerical Analysis" is here understood in its most general sense, as that part of Mathematics that covers:
1. The conception and mathematical analysis of efficient numerical schemes actually used on computers (the "core" of Numerical Analysis)
2. Optimization and Control Theory
3. Mathematical Modeling
4. The mathematical aspects of Scientific Computing
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