{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T09:37:28Z","timestamp":1772530648938,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","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>Amongst the more exciting phenomena in the field of nonlinear partial\n        differential equations is the Lavrentiev phenomenon which occurs in the calculus of\n        variations. We prove that a conforming finite element method fails if and only if the\n        Lavrentiev phenomenon is present. Consequently, nonstandard finite element methods\n        have to be designed for the detection of the Lavrentiev phenomenon in the computational\n        calculus of variations.\n        We formulate and analyze a general strategy for solving variational problems in the\n        presence of the Lavrentiev phenomenon based on a splitting and penalization strategy.\n        We establish convergence results under mild conditions on the stored energy function.\n        Moreover, we present practical strategies for the solution of the discretized problems\n        and for the choice of the penalty parameter.<\/jats:p>","DOI":"10.2478\/cmam-2010-0008","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:09:21Z","timestamp":1366042161000},"page":"137-163","source":"Crossref","is-referenced-by-count":11,"title":["Analysis of a Class of Penalty Methods for Computing Singular Minimizers"],"prefix":"10.2478","volume":"10","author":[{"given":"C.","family":"Carstensen","sequence":"first","affiliation":[{"name":"1Humboldt-Universit\u00a8at zu Berlin, Unter den Linden 6, 10099 Berlin, Germany."}]},{"given":"C.","family":"Ortner","sequence":"additional","affiliation":[{"name":"2Mathematical Institute, University of Oxford, 24-29 St Giles\u2019, Oxford OX1 3LB, UK."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/2\/article-p137.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2010-0008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:37Z","timestamp":1619101297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/2\/article-p137.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2010-0008","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2010]]}}}