{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T10:08:56Z","timestamp":1783937336117,"version":"3.55.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,4,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>\nIn this work, we derive a goal-oriented a posteriori error estimator for the error due to\ntime-discretization of nonlinear parabolic partial differential equations by the fractional step\ntheta method. This time-stepping scheme is assembled by three steps of the general theta method,\nthat also unifies simple schemes like forward and backward Euler as well as the Crank\u2013Nicolson\nmethod. Further, by combining three substeps of the theta time-stepping scheme, the fractional\nstep theta time-stepping scheme is derived. It possesses highly desired stability and numerical\ndissipation properties and is second order accurate.\nThe derived error estimator is based on a Petrov\u2013Galerkin formulation that is up to a numerical\nquadrature error equivalent to the theta time-stepping scheme. The error estimator is assembled\nas one weighted residual term given by the dual weighted residual method and one additional\nresidual estimating the Galerkin error between time-stepping scheme and Petrov\u2013Galerkin\nformulation.\n<\/jats:p>","DOI":"10.1515\/cmam-2014-0002","type":"journal-article","created":{"date-parts":[[2014,1,20]],"date-time":"2014-01-20T20:07:02Z","timestamp":1390248422000},"page":"203-230","source":"Crossref","is-referenced-by-count":21,"title":["Goal-Oriented Error Estimation for the Fractional Step Theta Scheme"],"prefix":"10.1515","volume":"14","author":[{"given":"Dominik","family":"Meidner","sequence":"first","affiliation":[{"name":"Chair of Optimal Control, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstr. 3, 85748 Garching, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Richter","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2014,1,16]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/2\/article-p203.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0002\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0002\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:32:36Z","timestamp":1680298356000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0002\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,13]]},"published-print":{"date-parts":[[2014,4,1]]}},"alternative-id":["10.1515\/cmam-2014-0002"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2014-0002","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,16]]}}}