{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:51:57Z","timestamp":1776837117260,"version":"3.51.2"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"344","license":[{"start":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T00:00:00Z","timestamp":1718841600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We introduce two a posteriori error estimators for N\u00e9d\u00e9lec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager\u2013Synge identity and an associated equilibration procedure. They are reliable and efficient, and the error estimates are polynomial-degree-robust. In addition, when the domain is convex, the reliability constants are fully computable. The proposed error estimators are also cheap and easy to implement, as they are computed by solving divergence-constrained minimization problems over edge patches. Numerical examples highlight our key findings, and show that both estimators are suited to drive adaptive refinement algorithms. Besides, these examples seem to indicate that guaranteed upper bounds can be achieved even in non-convex domains.<\/p>","DOI":"10.1090\/mcom\/3817","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T13:32:57Z","timestamp":1687267977000},"page":"2413-2437","source":"Crossref","is-referenced-by-count":2,"title":["A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem"],"prefix":"10.1090","volume":"92","author":[{"given":"T.","family":"Chaumont-Frelet","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics (Amsterdam)","isbn-type":"print","volume-title":"Sobolev spaces","volume":"140","author":"Adams, Robert A.","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0120441438","edition":"2"},{"key":"2","series-title":"Pure and Applied Mathematics (New York)","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824","volume-title":"A posteriori error estimation in finite element analysis","author":"Ainsworth, Mark","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/047129411X"},{"key":"3","series-title":"Advances in Numerical Mathematics","isbn-type":"print","volume-title":"Anisotropic finite elements: local estimates and applications","author":"Apel, Thomas","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/3519027445"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1051\/m2an\/1987210201991","article-title":"The \u210e-\ud835\udc5d version of the finite element method with quasi-uniform meshes","volume":"21","author":"Babu\u0161ka, I.","year":"1987","journal-title":"RAIRO Mod\\'{e}l. 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