{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T13:18:07Z","timestamp":1776863887451,"version":"3.51.2"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"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":[[2011]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> In this paper we consider a posteriori error estimates for space-time finite element \n\t\t\tdiscretizations for optimal control of hyperbolic partial dierential equations of second \n\t\t\torder. It is an extension of Meidner and Vexler (2007), where optimal control problems of \n\t\t\tparabolic equations are analyzed. The state equation is formulated as a first order system \n\t\t\tin time and a posteriori error estimates are derived separating the in uences of time, space, \n\t\t\tand control discretization. Using this information the accuracy of the solution is improved \n\t\t\tby local mesh refinement. Numerical examples are presented. Finally, we analyze the \n\t\t\tconservation of energy of the homogeneous wave equation with respect to dynamically in time \n\t\t\tchanging spatial meshes.<\/jats:p>","DOI":"10.2478\/cmam-2011-0012","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:15:03Z","timestamp":1366042503000},"page":"214-240","source":"Crossref","is-referenced-by-count":31,"title":["Adaptive Finite Element Methods For Optimal Control Of Second Order Hyperbolic Equations"],"prefix":"10.2478","volume":"11","author":[{"given":"Axel","family":"Kr\u00f6ner","sequence":"first","affiliation":[{"name":"1Lehrstuhl f\u00fcr Mathematische Optimierung, Technische Universit\u00e4t M\u00fcnchen, Fakult\u00e4t f\u00fcr Mathematik, Boltzmannstra\u00dfe 3, 85748 Garching b. M\u00fcnchen, Germany."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/11\/2\/article-p214.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2011-0012\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:53Z","timestamp":1619101313000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/11\/2\/article-p214.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2011-0012","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2011]]}}}