{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T05:42:59Z","timestamp":1769578979021,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,11,6]],"date-time":"2011-11-06T00:00:00Z","timestamp":1320537600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s00211-011-0422-z","type":"journal-article","created":{"date-parts":[[2011,11,5]],"date-time":"2011-11-05T09:40:49Z","timestamp":1320486049000},"page":"733-762","source":"Crossref","is-referenced-by-count":37,"title":["A-posteriori error estimates for optimal control problems with state and control constraints"],"prefix":"10.1007","volume":"120","author":[{"given":"Arnd","family":"R\u00f6sch","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Wachsmuth","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,11,6]]},"reference":[{"issue":"3","key":"422_CR1","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1137\/090778018","volume":"49","author":"T. Apel","year":"2011","unstructured":"Apel T., Benedix O., Sirch D., Vexler B.: A priori mesh grading for an elliptic problem with Dirac right-hand side. SIAM J. Numer. Anal. 49(3), 992\u20131005 (2011)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"422_CR2","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00211-006-0041-2","volume":"105","author":"R. Araya","year":"2006","unstructured":"Araya R., Behrens E., Rodr\u00edguez R.: A posteriori error estimates for elliptic problems with Dirac delta source terms. Numer. Math. 105(2), 193\u2013 (2006)","journal-title":"Numer. Math."},{"issue":"1","key":"422_CR3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10589-008-9200-y","volume":"44","author":"O. Benedix","year":"2009","unstructured":"Benedix O., Vexler B.: A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints. Comput. Optim. Appl. 44(1), 3\u201325 (2009)","journal-title":"Comput. Optim. Appl."},{"key":"422_CR4","volume-title":"Finite Elemente\u2014Theorie, Schnelle L\u00f6ser und Anwendungen in der Elastizit\u00e4tstheorie","author":"D. Braess","year":"1997","unstructured":"Braess D.: Finite Elemente\u2014Theorie, Schnelle L\u00f6ser und Anwendungen in der Elastizit\u00e4tstheorie. Springer, Berlin (1997)"},{"key":"422_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4338-8","volume-title":"The Mathematical Theory of Finite Element Methods","author":"S.C. Brenner","year":"1994","unstructured":"Brenner S.C., Scott L.R.: The Mathematical Theory of Finite Element Methods. Springer, New York (1994)"},{"issue":"6","key":"422_CR6","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1137\/0324078","volume":"24","author":"E. Casas","year":"1986","unstructured":"Casas E.: Control of an elliptic problem with pointwise state constraints. SIAM J. Control Optim. 24(6), 1309\u20131318 (1986)","journal-title":"SIAM J. Control Optim."},{"key":"422_CR7","doi-asserted-by":"crossref","unstructured":"Cherednichenko, S., Krumbiegel, K., R\u00f6sch, A.: Error estimates for the Lavrentiev regularization of elliptic optimal control problems. Inverse Probl. 24(5), 055003, 21 (2008)","DOI":"10.1088\/0266-5611\/24\/5\/055003"},{"key":"422_CR8","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0045-7825(73)90019-4","volume":"2","author":"P.G. Ciarlet","year":"1973","unstructured":"Ciarlet P.G., Raviart P.-A.: Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Eng. 2, 17\u201331 (1973)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"422_CR9","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1137\/060652361","volume":"45","author":"K. Deckelnick","year":"2007","unstructured":"Deckelnick K., Hinze M.: Convergence of a finite element approximation to a state-constrained elliptic control problem. SIAM J. Numer. Anal. 45(5), 1937\u20131953 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"422_CR10","volume-title":"Elliptic Problems in Nonsmooth Domains","author":"P. Grisvard","year":"1985","unstructured":"Grisvard P.: Elliptic Problems in Nonsmooth Domains. Pitman, London (1985)"},{"issue":"4","key":"422_CR11","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1515\/JNUM.2008.014","volume":"16","author":"A. G\u00fcnther","year":"2008","unstructured":"G\u00fcnther A., Hinze M.: A posteriori error control of a state constrained elliptic control problem. J. Numer. Math. 16(4), 307\u2013322 (2008)","journal-title":"J. Numer. Math."},{"key":"422_CR12","doi-asserted-by":"crossref","first-page":"5468","DOI":"10.1137\/090761823","volume":"48","author":"M. Hinterm\u00fcller","year":"2010","unstructured":"Hinterm\u00fcller M., Hoppe R.H.W.: Goal-oriented adaptivity in pointwise state constrained optimal control of partial differential equations. SIAM J. Control Optim. 48, 5468\u20135487 (2010)","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"422_CR13","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1051\/cocv:2007057","volume":"14","author":"M. Hinterm\u00fcller","year":"2008","unstructured":"Hinterm\u00fcller M., Hoppe R.H.W., Iliash Y., Kieweg M.: An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints. ESAIM Control Optim. Calc. Var. 14(3), 540\u2013560 (2008)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"422_CR14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10589-005-4559-5","volume":"30","author":"M. Hinze","year":"2005","unstructured":"Hinze M.: A variational discretization concept in control constrained optimization: the linear-quadratic case. J. Comput. Optim. Appl. 30, 45\u201363 (2005)","journal-title":"J. Comput. Optim. Appl."},{"key":"422_CR15","volume-title":"Optimization with PDE Constraints, Volume 23 of Mathematical Modelling: Theory and Applications","author":"M. Hinze","year":"2009","unstructured":"Hinze M., Pinnau R., Ulbrich M., Ulbrich S.: Optimization with PDE Constraints, Volume 23 of Mathematical Modelling: Theory and Applications. Springer, New York (2009)"},{"issue":"3","key":"422_CR16","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1515\/JNUM.2009.012","volume":"17","author":"R.H.W. Hoppe","year":"2009","unstructured":"Hoppe R.H.W., Kieweg M.: A posteriori error estimation of finite element approximations of pointwise state constrained distributed control problems. J. Numer. Math. 17(3), 219\u2013244 (2009)","journal-title":"J. Numer. Math."},{"issue":"1","key":"422_CR17","first-page":"17","volume":"18","author":"K. Krumbiegel","year":"2008","unstructured":"Krumbiegel K., R\u00f6sch A.: A new stopping criterion for iterative solvers for control constrained optimal control problems. Arch. Control Sci. 18(1), 17\u201342 (2008)","journal-title":"Arch. Control Sci."},{"issue":"2","key":"422_CR18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10915-007-9147-7","volume":"33","author":"R. Li","year":"2007","unstructured":"Li R., Liu W., Yan N.: A posteriori error estimates of recovery type for distributed convex optimal control problems. J. Sci. Comput. 33(2), 155\u2013182 (2007)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"422_CR19","first-page":"51","volume":"37","author":"C. Meyer","year":"2008","unstructured":"Meyer C.: Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints. Control Cybern. 37(1), 51\u201383 (2008)","journal-title":"Control Cybern."},{"key":"422_CR20","first-page":"251","volume":"37","author":"C. Meyer","year":"2008","unstructured":"Meyer C., de los Reyes J.C., Vexler B.: Finite element error analysis for state-constrained optimal control of the Stokes equations. Control Cybern. 37, 251\u2013284 (2008)","journal-title":"Control Cybern."},{"issue":"4","key":"422_CR21","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s00211-006-0027-0","volume":"104","author":"R.H. Nochetto","year":"2006","unstructured":"Nochetto R.H., Schmidt A., Siebert K.G., Veeser A.: Pointwise a posteriori error estimates for monotone semi-linear equations. Numer. Math. 104(4), 515\u2013538 (2006)","journal-title":"Numer. Math."},{"issue":"1\u20133","key":"422_CR22","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0024-3795(00)00273-1","volume":"324","author":"M. Plum","year":"2001","unstructured":"Plum M.: Computer-assisted enclosure methods for elliptic differential equations. Linear Algebra Appl. 324(1\u20133), 147\u2013187 (2001)","journal-title":"Linear Algebra Appl."},{"key":"422_CR23","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/112","volume-title":"Optimal Control of Partial Differential Equations, Volume 112 of Graduate Studies in Mathematics","author":"F. Tr\u00f6ltzsch","year":"2010","unstructured":"Tr\u00f6ltzsch F.: Optimal Control of Partial Differential Equations, Volume 112 of Graduate Studies in Mathematics. AMS, Providence (2010)"},{"issue":"1","key":"422_CR24","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s10589-008-9209-2","volume":"47","author":"W. Wollner","year":"2010","unstructured":"Wollner W.: A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints. Comput. Optim. Appl. 47(1), 133\u2013159 (2010)","journal-title":"Comput. Optim. Appl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-011-0422-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-011-0422-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-011-0422-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T03:53:57Z","timestamp":1560916437000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-011-0422-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,6]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["422"],"URL":"https:\/\/doi.org\/10.1007\/s00211-011-0422-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,11,6]]}}}