{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:09:26Z","timestamp":1760267366919,"version":"3.37.3"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"name":"DFG Research Center MATHEON"},{"name":"WCU program through KOSEF","award":["R31-2008-000-10049-0"],"award-info":[{"award-number":["R31-2008-000-10049-0"]}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["11271035, 91430213, 11421101"],"award-info":[{"award-number":["11271035, 91430213, 11421101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper provides a refined a posteriori error control for\nthe obstacle problem with an affine obstacle which allows\nfor a proof of optimal complexity of an adaptive algorithm.\nThis is the first adaptive mesh-refining\nfinite element method known to be of optimal\ncomplexity for some variational inequality.\nThe result holds for first-order conforming finite element methods in\nany spacial dimension\nbased on shape-regular triangulation into simplices for an affine obstacle.\nThe key contribution is the <jats:italic>discrete reliability<\/jats:italic> of the a\nposteriori error estimator from\n[Numer. Math. 107 (2007), 455\u2013471]\nin an edge-oriented modification which circumvents the difficulties caused\nby the non-existence of a positive second-order approximation\n[Math. Comp. 71 (2002), 1405\u20131419].<\/jats:p>","DOI":"10.1515\/cmam-2015-0017","type":"journal-article","created":{"date-parts":[[2015,6,15]],"date-time":"2015-06-15T17:00:24Z","timestamp":1434387624000},"page":"259-277","source":"Crossref","is-referenced-by-count":9,"title":["An Optimal Adaptive Finite Element Method for an Obstacle Problem"],"prefix":"10.1515","volume":"15","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Humboldt 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":"Jun","family":"Hu","sequence":"additional","affiliation":[{"name":"LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2015,6,13]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/15\/3\/article-p259.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0017\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0017\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T20:23:08Z","timestamp":1680294188000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0017\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,13]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,5,20]]},"published-print":{"date-parts":[[2015,7,1]]}},"alternative-id":["10.1515\/cmam-2015-0017"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0017","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2015,6,13]]}}}