Complexes from complexes: Finite element complexes in three dimensions.
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| Title: | Complexes from complexes: Finite element complexes in three dimensions. |
|---|---|
| Authors: | Chen, Long1 (AUTHOR), Huang, Xuehai2 (AUTHOR) |
| Source: | Mathematics of Computation. May2026, Vol. 95 Issue 359, p1083-1142. 60p. |
| Subjects: | Finite element method, Mathematical complexes, Partial differential equations, Elasticity |
| Abstract: | In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as shown by Arnold and Hu [Found. Comput. Math. 21 (2021), pp. 1739–1774]. This paper extends their approach to three-dimensional finite element complexes. The finite element Hessian, elasticity, and divdiv complexes are systematically derived by applying techniques such as smooth finite element de Rham complexes, the t-n decomposition, and trace complexes, along with related two-dimensional finite element analogs. The construction includes two reduction operations and one augmentation operation to address continuity differences in the BGG diagram, ultimately resulting in a comprehensive and effective framework for constructing finite element complexes, which have various applications in PDE solving. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Computation is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Complexes from complexes: Finite element complexes in three dimensions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chen%2C+Long%22">Chen, Long</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Huang%2C+Xuehai%22">Huang, Xuehai</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Computation%22">Mathematics of Computation</searchLink>. May2026, Vol. 95 Issue 359, p1083-1142. 60p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+complexes%22">Mathematical complexes</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as shown by Arnold and Hu [Found. Comput. Math. 21 (2021), pp. 1739–1774]. This paper extends their approach to three-dimensional finite element complexes. The finite element Hessian, elasticity, and divdiv complexes are systematically derived by applying techniques such as smooth finite element de Rham complexes, the t-n decomposition, and trace complexes, along with related two-dimensional finite element analogs. The construction includes two reduction operations and one augmentation operation to address continuity differences in the BGG diagram, ultimately resulting in a comprehensive and effective framework for constructing finite element complexes, which have various applications in PDE solving. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Computation is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1090/mcom/4079 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 60 StartPage: 1083 Subjects: – SubjectFull: Finite element method Type: general – SubjectFull: Mathematical complexes Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Elasticity Type: general Titles: – TitleFull: Complexes from complexes: Finite element complexes in three dimensions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chen, Long – PersonEntity: Name: NameFull: Huang, Xuehai IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00255718 Numbering: – Type: volume Value: 95 – Type: issue Value: 359 Titles: – TitleFull: Mathematics of Computation Type: main |
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