{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:19:03Z","timestamp":1776788343168,"version":"3.51.2"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"264","license":[{"start":{"date-parts":[[2009,4,28]],"date-time":"2009-04-28T00:00:00Z","timestamp":1240876800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin\u2013Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.<\/p>","DOI":"10.1090\/s0025-5718-08-02116-9","type":"journal-article","created":{"date-parts":[[2008,7,25]],"date-time":"2008-07-25T12:55:42Z","timestamp":1216990542000},"page":"1917-1939","source":"Crossref","is-referenced-by-count":8,"title":["Robust a posteriori error estimation for the nonconforming Fortin\u2013Soulie finite element approximation"],"prefix":"10.1090","volume":"77","author":[{"given":"Mark","family":"Ainsworth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard","family":"Rankin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2008,4,28]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"2320","DOI":"10.1137\/S0036142903425112","article-title":"Robust a posteriori error estimation for nonconforming finite element approximation","volume":"42","author":"Ainsworth, Mark","year":"2005","journal-title":"SIAM J. 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