{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T18:25:41Z","timestamp":1768760741102,"version":"3.49.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,1,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nThis survey compares different strategies for guaranteed error control\nfor the lowest-order nonconforming Crouzeix\u2013Raviart finite element method for the Stokes equations.\nThe upper error bound involves the minimal distance of the computed piecewise gradient\n<jats:inline-formula id=\"eq1_w2aab2b8b8b1b7b1aab1c12b1b1Aa\"><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2013-0021_fafc399a9f5871bfa5fac338ac32ea53.png\"\/><jats:tex-math>$\\operatorname{D}_{\\textup {NC}}u_{\\textup {CR}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>\nto the gradients of Sobolev functions with exact boundary conditions.\nSeveral improved suggestions for\nthe cheap computation of such test functions\ncompete in five benchmark examples. This paper provides numerical evidence that guaranteed\nerror control of the\nnonconforming FEM is indeed possible for the Stokes equations with overall efficiency indices\nbetween 1 to 4 in the asymptotic range.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0021","type":"journal-article","created":{"date-parts":[[2014,1,9]],"date-time":"2014-01-09T20:13:43Z","timestamp":1389298423000},"page":"35-54","source":"Crossref","is-referenced-by-count":12,"title":["Computational Survey on A Posteriori Error Estimators for the Crouzeix\u2013Raviart Nonconforming Finite Element Method for the Stokes Problem"],"prefix":"10.1515","volume":"14","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[{"name":"1Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099 Berlin, Germany; and Department of Computational Science and Engineering, Yonsei University, 120-749 Seoul, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Merdon","sequence":"additional","affiliation":[{"name":"2Weierstra\u00df-Institut, Mohrenstr. 39, 10117 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/1\/article-p35.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/14\/1\/article-p35.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:46Z","timestamp":1614481426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0021\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0021","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}