{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:06:58Z","timestamp":1760267218014},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2010]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> We consider the conforming of finite element approximations of reactiondiffusion\nproblems. We propose new a posteriori error estimators based on H(div)-\nconforming finite elements and equilibrated fluxes. It is shown that these estimators\ngive rise to an upper bound where the constant is one in front of the indicator, up to\nhigher order terms. Lower bounds can also be established with constants depending on\nthe shape regularity of the mesh and the local variation of the coefficients. We further\nanalyze the convergence of an adaptive algorithm. The reliability and efficiency of the\nproposed estimators are confirmed by various numerical tests.<\/jats:p>","DOI":"10.2478\/cmam-2010-0002","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:13:17Z","timestamp":1366042397000},"page":"49-68","source":"Crossref","is-referenced-by-count":6,"title":["A Posteriori Error Estimators Based on Equilibrated Fluxes"],"prefix":"10.2478","volume":"10","author":[{"given":"Sarah","family":"Cochez-Dhondt","sequence":"first","affiliation":[{"name":"1Univ Lille Nord de France, F-59000 Lille, France; UVHC, LAMAV, F-59313 Valenciennes, France."}]},{"given":"Serge","family":"Nicaise","sequence":"additional","affiliation":[{"name":"2CNRS, FR 2956, F-59655 Villeneuve d\u2019Ascq, France."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/1\/article-p49.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2010-0002\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:34Z","timestamp":1619101294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/1\/article-p49.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2010-0002","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2010]]}}}