{"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/adaptive-finite-element-methods-based-on-flux","title":"Adaptive finite element methods based on flux and stress equilibration using FEniCSx","arxiv_id":"2410.09764","date":"2024-10-13","proceeding":null,"authors":["Maximilian Brodbeck","Fleurianne Bertrand","Tim Ricken"],"abstract":"This contribution shows how a-posteriori error estimators based on equilibrated fluxes - H(div) functions fulfilling the underlying conservation law - can be implemented in FEniCSx. Therefore, dolfinx_eqlb is introduced, its algorithmic structure is described and classical benchmarks for adaptive solution procedures for the Poisson problem and linear elasticity are presented.","url_abs":"https://arxiv.org/abs/2410.09764v1","url_pdf":"https://arxiv.org/pdf/2410.09764v1.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":"adaptive-finite-element-methods-based-on-flux","repo_url":"https://github.com/brodbeck-m/afem-by-equilibration","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"adaptive-finite-element-methods-based-on-flux","repo_url":"https://github.com/brodbeck-m/dolfinx_eqlb","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}