{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T01:47:23Z","timestamp":1743040043230,"version":"3.40.3"},"publisher-location":"Basel","reference-count":18,"publisher":"Springer Basel","isbn-type":[{"type":"print","value":"9783034801324"},{"type":"electronic","value":"9783034801331"}],"license":[{"start":{"date-parts":[[2011,10,28]],"date-time":"2011-10-28T00:00:00Z","timestamp":1319760000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2011,10,28]],"date-time":"2011-10-28T00:00:00Z","timestamp":1319760000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-0348-0133-1_20","type":"book-chapter","created":{"date-parts":[[2012,1,2]],"date-time":"2012-01-02T10:34:06Z","timestamp":1325500446000},"page":"377-389","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Priori Mesh Grading for Distributed Optimal Control Problems"],"prefix":"10.1007","author":[{"given":"Thomas","family":"Apel","sequence":"first","affiliation":[]},{"given":"Dieter","family":"Sirch","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,10,28]]},"reference":[{"key":"20_CR1","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10092-007-0133-0","volume":"44","author":"Th Apel","year":"2007","unstructured":"Th. Apel and A. R\u00f6sch and G. Winkler, Optimal control in non-convex domains: a priori discretization error estimates. Calcolo, 44 (2007), 137\u2013158.","journal-title":"Calcolo"},{"key":"20_CR2","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10492-011-0002-7","volume":"56","author":"Th Apel","year":"2011","unstructured":"Th. Apel and D. Sirch, \ud835\udc3f\n2-error estimates for the Dirichlet and Neumann problem on anisotropic finite element meshes. Appl. Math. 56 (2011), 177\u2013206.","journal-title":"Appl. Math."},{"key":"20_CR3","unstructured":"Th. Apel, D. Sirch and G. Winkler, Error estimates for control constrained optimal control problems: Discretization with anisotropic finite element meshes. DFGPriority Program 1253, 2008, preprint, SPP1253-02-06, Erlangen."},{"key":"20_CR4","doi-asserted-by":"publisher","first-page":"2050","DOI":"10.1016\/j.apnum.2008.12.003","volume":"59","author":"Th Apel","year":"2009","unstructured":"Th. Apel and G. Winkler, Optimal control under reduced regularity. Appl. Numer. Math., 59 (2009), 2050\u20132064.","journal-title":"Appl. Numer. Math."},{"key":"20_CR5","doi-asserted-by":"crossref","unstructured":"P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, 1978.","DOI":"10.1115\/1.3424474"},{"key":"20_CR6","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10589-005-4559-5","volume":"30","author":"M Hinze","year":"2005","unstructured":"M. Hinze, A variational discretization concept in control constrained optimization: The linear-quadratic case. Comput. Optim. Appl., 30 (2005), 45\u201361.","journal-title":"Comput. Optim. Appl."},{"key":"20_CR7","unstructured":"M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE Constraints. Springer, 2008."},{"key":"20_CR8","first-page":"391","volume-title":"International Series of Numerical Mathematics","author":"M Hinze","year":"2011","unstructured":"M. Hinze and A. R\u00f6sch, Discretization of optimal control problems. International Series of Numerical Mathematics, Vol. 160 (this volume), Springer, Basel, 2011, 391\u2013430."},{"key":"20_CR9","volume-title":"Some Applications of Weighted Sobolev Spaces","author":"A Kufner","year":"1987","unstructured":"A. Kufner and A.-M. S\u00e4ndig, Some Applications of Weighted Sobolev Spaces. Teubner, Leipzig, 1987."},{"key":"20_CR10","unstructured":"J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer, 1971. Translation of the French edition \u201cContr\u00f4le optimal de syst\u00e8mes gouvern\u00e9s par de \u00e9quations aux d\u00e9riv\u00e9es partielles\u201d, Dunod and Gauthier-Villars, 1968."},{"key":"20_CR11","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF01447752","volume":"8","author":"K Malanowski","year":"1981","unstructured":"K. Malanowski, Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems. Appl. Math. Optim., 8 (1981), 69\u201395.","journal-title":"Appl. Math. Optim."},{"key":"20_CR12","doi-asserted-by":"publisher","first-page":"335","DOI":"10.4171\/ZAA\/71","volume":"2","author":"VG Maz\u2019ya","year":"1983","unstructured":"V.G. Maz\u2019ya and B.A. Plamenevsky, The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries, part I, II. Z. Anal. Anwend., 2 (1983), 335\u2013359, 523\u2013551. In Russian.","journal-title":"Z. Anal. Anwend."},{"key":"20_CR13","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1080\/00036810310001632871","volume":"83","author":"VG Maz\u2019ya","year":"2004","unstructured":"V.G. Maz\u2019ya and J. Rossmann, Schauder estimates for solutions to boundary value problems for second-order elliptic systems in polyhedral domains. Applicable Analysis, 83 (2004), 271\u2013308.","journal-title":"Applicable Analysis"},{"key":"20_CR14","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1137\/S0363012903431608","volume":"43","author":"C Meyer","year":"2004","unstructured":"C. Meyer and A. R\u00f6sch, Superconvergence properties of optimal control problems. SIAM J. Control Optim., 43 (2004), 970\u2013985.","journal-title":"SIAM J. Control Optim."},{"key":"20_CR15","volume-title":"Polygonal Interface Problems","author":"S Nicaise","year":"1993","unstructured":"S. Nicaise, Polygonal Interface Problems. Peter Lang GmbH, Europ\u00e4ischer Verlag der Wissenschaften, volume 39 of Methoden und Verfahren der mathematischen Physik, Frankfurt\/M., 1993."},{"key":"20_CR16","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/s10589-009-9305-y","volume":"49","author":"S Nicaise","year":"2011","unstructured":"S. Nicaise and D. Sirch, Optimal control of the Stokes equations: Conforming and non-conforming finite element methods under reduced regularity. Comput. Optim. Appl. 49 (2011), 567\u2013600.","journal-title":"Comput. Optim. Appl."},{"key":"20_CR17","volume-title":"Finite element error analysis for PDE-constrained optimal control problems: The control constrained case under reduced regularity","author":"D Sirch","year":"2010","unstructured":"D. Sirch, Finite element error analysis for PDE-constrained optimal control problems: The control constrained case under reduced regularity. TU M\u00fcnchen, 2010, \nhttp:\/\/mediatum2.ub.tum.de\/node?id=977779"},{"key":"20_CR18","volume-title":"Control constrained optimal control problems in non-convex threedimensional polyhedral domains","author":"G Winkler","year":"2008","unstructured":"G. Winkler, Control constrained optimal control problems in non-convex threedimensional polyhedral domains. PhD thesis, TU Chemnitz, 2008. \nhttp:\/\/archiv.tu-chemnitz.de\/pub\/2008\/0062"}],"container-title":["International Series of Numerical Mathematics","Constrained Optimization and Optimal Control for Partial Differential Equations"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-0348-0133-1_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T07:37:26Z","timestamp":1597304246000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-0348-0133-1_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,28]]},"ISBN":["9783034801324","9783034801331"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-0348-0133-1_20","relation":{},"ISSN":["0373-3149","2296-6072"],"issn-type":[{"type":"print","value":"0373-3149"},{"type":"electronic","value":"2296-6072"}],"subject":[],"published":{"date-parts":[[2011,10,28]]},"assertion":[{"value":"28 October 2011","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}