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The estimator is based on equilibration of the magnetic field and only involves small local problems that can be solved in parallel. Such an error estimator is already available for the lowest-degree N\u00e9d\u00e9lec element (Braess and Sch\u00f6berl in Math Comput 77(262):651-672, 2008) and requires solving local problems on vertex patches. The novelty of our estimator is that it can be applied to N\u00e9d\u00e9lec elements of arbitrary degree. Furthermore, our estimator does not require solving problems on vertex patches, but instead requires solving problems on only single elements, single faces, and very small sets of nodes. We prove reliability and efficiency of the estimator and present several numerical examples that confirm this.<\/jats:p>","DOI":"10.1007\/s10915-020-01224-x","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T12:03:04Z","timestamp":1591704184000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["An Equilibrated a Posteriori Error Estimator for Arbitrary-Order N\u00e9d\u00e9lec Elements for Magnetostatic Problems"],"prefix":"10.1007","volume":"83","author":[{"given":"Joscha","family":"Gedicke","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sjoerd","family":"Geevers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilaria","family":"Perugia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,9]]},"reference":[{"key":"1224_CR1","volume-title":"Anisotropic Finite Elements: Local Estimates and Applications","author":"T Apel","year":"1999","unstructured":"Apel, T.: Anisotropic Finite Elements: Local Estimates and Applications. 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