Finite elements for symmetric and traceless tensors in three dimensions

[2311.16077] Finite elements for symmetric and traceless tensors in three dimensions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2311.16077 (math) [Submitted on 27 Nov 2023 ( v1 ), last revised 13 Apr 2026 (this version, v3)] Title: Finite elements for symmetric and traceless tensors in three dimensions Authors: Kaibo Hu , Ting Lin , Bowen Shi View a PDF of the paper titled Finite elements for symmetric and traceless tensors in three dimensions, by Kaibo Hu and 2 other authors View PDF HTML (experimental) Abstract: We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector fields and symmetric and traceless tensor fields, connected through the conformal Killing operator, the linearized Cotton-York operator, and the divergence operator, respectively. This leads to discrete versions of transverse traceless (TT) tensors, i.e., symmetric, traceless and divergence-free matrix fields, in continuum mechanics and general relativity. We also show the inf-sup stability of the $H(\operatorname{div})$-conforming finite element symmetric and traceless tensors paired with discontinuous vectors. Comments: 56 pages, 2 figure Subjects: Numerical Analysis (math.NA) Cite as: arXiv:2311.16077 [math.NA] (or arXiv:2311.16077v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.2311.16077 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bowen Shi [ view email ] [v1] Mon, 27 Nov 2023 18:48:16 UTC (54 KB) [v2] Wed, 1 Oct 2025 04:07:55 UTC (177 KB) [v3] Mon, 13 Apr 2026 18:24:29 UTC (172 KB) Full-text links: Access Paper: View a PDF of the paper titled Finite elements for symmetric and traceless tensors in three dimensions, by Kaibo Hu and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2023-11 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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