{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/variational-multiscale-modeling-with-1","title":"Variational multiscale modeling with discretely divergence-free subscales: Non-divergence-conforming discretizations","arxiv_id":"2112.09823","date":"2021-12-18","proceeding":null,"authors":["Sajje Lee Calfy","John A. Evans","David Kamensky"],"abstract":"A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, \"Variational multiscale modeling with discretely divergence-free subscales\", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element method for the incompressible Navier-Stokes equations, which combined residual-based stabilization of advection, energetic stability, and satisfaction of a discrete incompressibility condition. However, the convergence analysis and numerical tests of the cited work were subject to the restrictive assumption of a divergence-conforming choice of velocity and pressure spaces, where the pressure space must contain the divergence of every velocity function. The present work extends the convergence analysis to arbitrary inf-sup-stable velocity-pressure pairs (while maintaining robustness in the advection-dominated regime) and demonstrates the convergence of the method numerically, using both the traditional and isogeometric Taylor-Hood elements.","url_abs":"https://arxiv.org/abs/2112.09823v1","url_pdf":"https://arxiv.org/pdf/2112.09823v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"variational-multiscale-modeling-with-1","repo_url":"https://github.com/david-kamensky/discretely-div-free-subscales","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}