{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T21:55:55Z","timestamp":1775858155202,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,11,7]],"date-time":"2007-11-07T00:00:00Z","timestamp":1194393600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2009,5]]},"DOI":"10.1007\/s10589-007-9129-6","type":"journal-article","created":{"date-parts":[[2007,11,6]],"date-time":"2007-11-06T19:44:41Z","timestamp":1194378281000},"page":"133-150","source":"Crossref","is-referenced-by-count":5,"title":["Finite-difference discretizations of quadratic control problems governed by ordinary elliptic differential equations"],"prefix":"10.1007","volume":"43","author":[{"given":"Walter","family":"Alt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nils","family":"Br\u00e4utigam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,11,7]]},"reference":[{"key":"9129_CR1","first-page":"1","volume":"3","author":"W. Alt","year":"2003","unstructured":"Alt, W.: Approximation of optimal control problems with bound constraints by control parameterization. Control Cybern. 3, 1\u201322 (2003)","journal-title":"Control Cybern."},{"key":"9129_CR2","doi-asserted-by":"crossref","first-page":"7","DOI":"10.7151\/dmdico.1073","volume":"27","author":"W. Alt","year":"2007","unstructured":"Alt, W., Br\u00e4utigam, N., R\u00f6sch, A.: Error estimates for finite element approximations of elliptic control problems. Discuss. Math. Differ. Incl. Control Optim. 27, 7\u201322 (2007)","journal-title":"Discuss. Math. Differ. Incl. Control Optim."},{"key":"9129_CR3","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1023\/A:1020576801966","volume":"23","author":"N. Arada","year":"2002","unstructured":"Arada, N., Casas, E., Tr\u00f6ltzsch, F.: Error estimates for the numerical approximation of a semilinear elliptic control problem. Comput. Optim. Appl. 23, 201\u2013229 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9129_CR4","unstructured":"Br\u00e4utigam, N.: Diskretisierung elliptischer Steuerungsprobleme. Ph.D. Thesis, Jena (2006)"},{"key":"9129_CR5","unstructured":"Br\u00e4utigam, N.: Discretization of elliptic control problems by finite elements. Technical Report, Jena (2006)"},{"key":"9129_CR6","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/978-0-387-35690-7_10","volume-title":"Analysis and Optimization of Differential Systems","author":"E. Casas","year":"2003","unstructured":"Casas, E., Tr\u00f6ltzsch, F.: Error estimates for linear-quadratic elliptic control problems. In: Barbu, V. et al. (eds.) Analysis and Optimization of Differential Systems, pp. 89\u2013100. Kluwer Academic, Boston (2003)"},{"key":"9129_CR7","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10589-005-2180-2","volume":"31","author":"E. Casas","year":"2005","unstructured":"Casas, E., Mateos, M., Tr\u00f6ltzsch, F.: Error estimates for the numerical approximation of boundary semilinear elliptic control problems for linear-quadratic elliptic control problems. Comput. Optim. Appl. 31, 193\u2013220 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"9129_CR8","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1987","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1987)"},{"key":"9129_CR9","series-title":"Lecture Notes in Control and Information Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0043612","volume-title":"Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems","author":"A.L. Dontchev","year":"1983","unstructured":"Dontchev, A.L.: Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems. Lecture Notes in Control and Information Sciences. vol.\u00a052. Springer, Berlin (1983)"},{"key":"9129_CR10","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1137\/S0036142999351765","volume":"38","author":"A.L. Dontchev","year":"2000","unstructured":"Dontchev, A.L., Hager, W.W., Veliov, V.V.: Second-order Runge-Kutta approximations in control constrained optimal control. SIAM J. Numer. Anal. 38, 202\u2013226 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"9129_CR11","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1080\/01630560008816979","volume":"21","author":"A.L. Dontchev","year":"2000","unstructured":"Dontchev, A.L., Hager, W.W., Malanowski, K.: Error bounds for Euler approximation of state and control constrained optimal control problem. Numer. Funct. Anal. Optim. 21, 653\u2013682 (2000)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9129_CR12","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1137\/0727063","volume":"17","author":"W.W. Hager","year":"1990","unstructured":"Hager, W.W.: Multiplier methods for nonlinear optimal control. SIAM J. Numer. Anal. 17, 1061\u20131080 (1990)","journal-title":"SIAM J. Numer. Anal."},{"key":"9129_CR13","doi-asserted-by":"crossref","unstructured":"Gro\u00dfmann, C., Roos, H.-G.: Numerik partieller Differentialgleichungen. Teubner (2005)","DOI":"10.1007\/978-3-322-80153-1"},{"key":"9129_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. Comput. Optim. Appl. 30, 45\u201361 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"9129_CR15","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01447752","volume":"8","author":"K. Malanowski","year":"1981","unstructured":"Malanowski, K.: Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal control problems. Appl. Math. Optim. 8, 69\u201395 (1981)","journal-title":"Appl. Math. Optim."},{"key":"9129_CR16","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1137\/S0363012903431608","volume":"43","author":"C. Meyer","year":"2004","unstructured":"Meyer, C., R\u00f6sch, A.: Superconvergence properties of optimal control problems. SIAM J. Control. Optim. 43, 970\u2013985 (2004)","journal-title":"SIAM J. Control. Optim."},{"key":"9129_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-56191-7","volume-title":"Numerische Mathematik 2","author":"A. Quarteroni","year":"2002","unstructured":"Quarteroni, A., Sacco, R., Saleri, F.: Numerische Mathematik 2, Springer, Berlin (2002)"},{"key":"9129_CR18","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/10556780500094945","volume":"21","author":"A. R\u00f6sch","year":"2006","unstructured":"R\u00f6sch, A.: Error estimates for linear-quadratic control problems with control constraints. Optim. Methods Softw. 21, 121\u2013134 (2006)","journal-title":"Optim. Methods Softw."},{"key":"9129_CR19","doi-asserted-by":"crossref","unstructured":"Samarskij, A.A.: Theorie der Differenzenverfahren. Akad. Verlagsgesellschaft (1984)","DOI":"10.1515\/9783112713952"},{"key":"9129_CR20","volume-title":"The Averaged Moduli of Smoothness","author":"B. Sendov","year":"1988","unstructured":"Sendov, B., Popov, V.A.: The Averaged Moduli of Smoothness. Wiley\u2013Interscience, New York (1988)"},{"key":"9129_CR21","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/BF00933141","volume":"29","author":"H.R. Sirisena","year":"1979","unstructured":"Sirisena, H.R., Chou, F.S.: Convergence of the control parameterization Ritz method for nonlinear optimal control problems. J. Optim. Theory Appl. 29, 369\u2013382 (1979)","journal-title":"J. Optim. Theory Appl."},{"key":"9129_CR22","doi-asserted-by":"crossref","unstructured":"Tr\u00f6ltzsch, F.: Optimale Steuerung partieller Differentialgleichungen. Vieweg (2005)","DOI":"10.1007\/978-3-322-96844-9"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9129-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-007-9129-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9129-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T03:53:15Z","timestamp":1737517995000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-007-9129-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,7]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,5]]}},"alternative-id":["9129"],"URL":"https:\/\/doi.org\/10.1007\/s10589-007-9129-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,7]]}}}