{"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/a-polytopal-method-for-the-brinkman-problem","title":"A polytopal method for the Brinkman problem robust in all regimes","arxiv_id":"2301.03272","date":"2023-01-09","proceeding":null,"authors":["Daniele A. Di Pietro","Jérôme Droniou"],"abstract":"In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across the all regimes and provide extensive numerical validation.","url_abs":"https://arxiv.org/abs/2301.03272v3","url_pdf":"https://arxiv.org/pdf/2301.03272v3.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":"a-polytopal-method-for-the-brinkman-problem","repo_url":"https://github.com/jdroniou/HArDCore3D-release","is_official":1,"mentioned_in_paper":0,"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}