{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T18:23:08Z","timestamp":1781029388301,"version":"3.54.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,6,19]],"date-time":"2010-06-19T00:00:00Z","timestamp":1276905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1007\/s10915-010-9392-z","type":"journal-article","created":{"date-parts":[[2010,6,18]],"date-time":"2010-06-18T12:33:41Z","timestamp":1276864421000},"page":"182-203","source":"Crossref","is-referenced-by-count":39,"title":["A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints"],"prefix":"10.1007","volume":"46","author":[{"given":"Wei","family":"Gong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ningning","family":"Yan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,6,19]]},"reference":[{"issue":"239","key":"9392_CR1","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1090\/S0025-5718-02-01412-6","volume":"71","author":"S. Bartels","year":"2002","unstructured":"Bartels, S., Carstensen, C.: Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I. Low order conforming, nonconforming, and mixed FEM. Math. Comput. 71(239), 945\u2013969 (2002)","journal-title":"Math. Comput."},{"key":"9392_CR2","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1137\/S0363012999351097","volume":"39","author":"R. Becker","year":"2000","unstructured":"Becker, R., Kapp, H., Rannacher, R.: Adaptive finite element methods for optimal control of partial differential equations: Basic concept. SIAM J. Control Optim. 39, 113\u2013132 (2000)","journal-title":"SIAM J. Control Optim."},{"key":"9392_CR3","doi-asserted-by":"crossref","first-page":"1524","DOI":"10.1137\/S036301299529330X","volume":"35","author":"M. Bergounioux","year":"1997","unstructured":"Bergounioux, M., Kunisch, K.: Augmented Lagrangian techniques for elliptic state constrained optimal control problems. SIAM J. Control Optim. 35, 1524\u20131543 (1997)","journal-title":"SIAM J. Control Optim."},{"key":"9392_CR4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1023\/A:1015489608037","volume":"22","author":"M. Bergounioux","year":"2002","unstructured":"Bergounioux, M., Kunisch, K.: Primal-dual strategy for state-constrained optimal control problems. Comput. Optim. Appl. 22, 193\u2013224 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9392_CR5","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0167-6911(02)00262-1","volume":"48","author":"M. Bergounioux","year":"2003","unstructured":"Bergounioux, M., Kunisch, K.: On the structure of Lagrange multipliers for state-constrained optimal control problems. Syst. Control Lett. 48, 169\u2013176 (2003)","journal-title":"Syst. Control Lett."},{"issue":"6","key":"9392_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":"9392_CR7","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1051\/cocv:2002049","volume":"8","author":"E. Casas","year":"2002","unstructured":"Casas, E.: Error estimate for the numerical approximation of semilinear elliptic control problems with finitely many state constraint. ESAIM Control Optim. Calc. Var. 8, 345\u2013374 (2002)","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"1","key":"9392_CR8","first-page":"67","volume":"21","author":"E. Casas","year":"2002","unstructured":"Casas, E., Mateos, M.: Uniform convergence of the FEM. Applications to state constrained control problems. Comput. Appl. Math. 21(1), 67\u2013100 (2002)","journal-title":"Comput. Appl. Math."},{"key":"9392_CR9","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s002110050009","volume":"84","author":"Z.M. Chen","year":"2000","unstructured":"Chen, Z.M., Nochetto, R.H.: Residual type a posteriori error estimates for elliptic obstacle problem. Numer. Math. 84, 527\u2013548 (2000)","journal-title":"Numer. Math."},{"issue":"5","key":"9392_CR10","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/24\/5\/055003","volume":"24","author":"S. Cherednichenko","year":"2008","unstructured":"Cherednichenko, S., Krumbiegel, K., R\u00f6sch, A.: Error estimates for the Lavrentiev regularization of elliptic optimal control problems. Inverse Probl. 24(5), 055003 (2008)","journal-title":"Inverse Probl."},{"key":"9392_CR11","first-page":"77","volume":"9","author":"Ph. Cl\u00e9ment","year":"1975","unstructured":"Cl\u00e9ment, Ph.: Approximation by finite element functions using local regularization. RAIRO Anal. Numer. 9, 77\u201384 (1975)","journal-title":"RAIRO Anal. Numer."},{"key":"9392_CR12","doi-asserted-by":"crossref","first-page":"1937\u20131953","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, 1937\u20131953 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9392_CR13","first-page":"297","volume":"26","author":"W. Gong","year":"2008","unstructured":"Gong, W., Li, R., Yan, N.N., Zhao, W.B.: An improved error analysis for finite element approximation of bioluminescence tomography. J. Comput. Math. 26(3), 297\u2013309 (2008)","journal-title":"J. Comput. Math."},{"issue":"1","key":"9392_CR14","first-page":"68","volume":"27","author":"W. Gong","year":"2009","unstructured":"Gong, W., Yan, N.N.: A posteriori error estimate for boundary control problems governed by the parabolic partial differential equations. J. Comput. Math. 27(1), 68\u201388 (2009)","journal-title":"J. Comput. Math."},{"key":"9392_CR15","volume-title":"Numerical Analysis of Variational Inequalities","author":"R. Glowinski","year":"1981","unstructured":"Glowinski, R., Lions, J.L., Tr\u00e9moli\u00e8res, R.: Numerical Analysis of Variational Inequalities. North-Holland, Amsterdam (1981)"},{"key":"9392_CR16","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s002110050048","volume":"68","author":"B.S. He","year":"1994","unstructured":"He, B.S.: Solving a class of linear projection equations. Numer. Math. 68, 71\u201380 (1994)","journal-title":"Numer. Math."},{"issue":"4","key":"9392_CR17","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1137\/070683891","volume":"47","author":"M. Hinterm\u00fcller","year":"2008","unstructured":"Hinterm\u00fcller, M., Hoppe, R.H.W.: Goal-oriented adaptivity in control constrained optimal control of partial differential equations. SIAM J. Control Optim. 47(4), 1721\u20131743 (2008)","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"9392_CR18","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1137\/S1052623401383558","volume":"13","author":"M. Hinterm\u00fcller","year":"2002","unstructured":"Hinterm\u00fcller, M., Ito, K., Kunisch, K.: The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13(3), 865\u2013888 (2002)","journal-title":"SIAM J. Optim."},{"key":"9392_CR19","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1137\/080737265","volume":"20","author":"M. Hinterm\u00fcller","year":"2009","unstructured":"Hinterm\u00fcller, M., Kunisch, K.: Stationary optimal control problems with pointwise state constraints. SIAM J. Optim. 20, 1133\u20131156 (2009)","journal-title":"SIAM J. Optim."},{"key":"9392_CR20","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s00211-004-0531-z","volume":"98","author":"M. Hinterm\u00fcller","year":"2004","unstructured":"Hinterm\u00fcller, M., Ring, W.: A level set approach for the solution of a state-constrained optimal control problem. Numer. Math. 98, 135\u2013166 (2004)","journal-title":"Numer. Math."},{"issue":"3","key":"9392_CR21","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0167-6911(03)00156-7","volume":"50","author":"K. Ito","year":"2003","unstructured":"Ito, K., Kunisch, K.: Semi-smooth Newton methods for state-constrained optimal control problems. Syst. Control Lett. 50(3), 221\u2013228 (2003)","journal-title":"Syst. Control Lett."},{"key":"9392_CR22","series-title":"Lectures Notes in Pure and Applied Mathematics","volume-title":"Finite Element Methods: Superconvergence, Post-processing, and A Posteriori Estimates","year":"1998","unstructured":"K\u0159\u00ed\u017eek, M., Neittaanmaki, P., Stenberg, R. (eds.): Finite Element Methods: Superconvergence, Post-processing, and A Posteriori Estimates. Lectures Notes in Pure and Applied Mathematics, vol.\u00a0196. Dekker, New York (1998)"},{"key":"9392_CR23","unstructured":"Lin, Q., Yan, N.: Structure and Analysis for Efficient Finite Element Methods. Publishers of Hebei University (in Chinese) (1996)"},{"key":"9392_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65024-6","volume-title":"Optimal Control of Systems Governed by Partial Differential Equations","author":"J.L. Lions","year":"1971","unstructured":"Lions, J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, Berlin (1971)"},{"issue":"1","key":"9392_CR25","first-page":"97","volume":"27","author":"W.B. Liu","year":"2009","unstructured":"Liu, W.B., Gong, W., Yan, N.N.: A new finite element approximation of a state-constrained optimal control problem. J. Comput. Math. 27(1), 97\u2013114 (2009)","journal-title":"J. Comput. Math."},{"issue":"1\u20134","key":"9392_CR26","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1023\/A:1014239012739","volume":"15","author":"W.B. Liu","year":"2001","unstructured":"Liu, W.B., Yan, N.N.: A posteriori error analysis for convex distributed optimal control problems. Adv. Comput. Math. 15(1\u20134), 285\u2013309 (2001)","journal-title":"Adv. Comput. Math."},{"key":"9392_CR27","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1137\/S0036142901384009","volume":"40","author":"W.B. Liu","year":"2003","unstructured":"Liu, W.B., Yan, N.N.: A posteriori error estimates for optimal problems governed by Stokes equations. SIAM J. Numer. Anal. 40, 1850\u20131869 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"9392_CR28","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s002110100380","volume":"93","author":"W.B. Liu","year":"2003","unstructured":"Liu, W.B., Yan, N.N.: A posteriori error estimates for optimal control problems governed by parabolic equations. Numer. Math. 93, 497\u2013521 (2003)","journal-title":"Numer. Math."},{"key":"9392_CR29","volume-title":"Adaptive Finite Element Methods for Optimal Control Governed by PDEs","author":"W.B. Liu","year":"2008","unstructured":"Liu, W.B., Yan, N.N.: Adaptive Finite Element Methods for Optimal Control Governed by PDEs. Science Press, Beijing (2008)"},{"key":"9392_CR30","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, 51\u201385 (2008)","journal-title":"Control Cybern."},{"key":"9392_CR31","series-title":"Lecture Notes in Pure and Appl. Math.","first-page":"231","volume-title":"Control of Partial Differential Equations and Applications","author":"M. Pierre","year":"1996","unstructured":"Pierre, M., Sokolowsky, J.: Differentiability of projection and applications. In: Control of Partial Differential Equations and Applications, Laredo, 1994. Lecture Notes in Pure and Appl. Math., vol.\u00a0174, pp. 231\u2013240. Dekker, New York (1996)"},{"issue":"240","key":"9392_CR32","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1090\/S0025-5718-01-01369-2","volume":"71","author":"R.H. Nochetto","year":"2002","unstructured":"Nochetto, R.H., Wahlbin, L.B.: Positivity preserving finite element approximation. Math. Comp. 71(240), 1405\u20131419 (2002)","journal-title":"Math. Comp."},{"key":"9392_CR33","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0025-5718-1990-1011446-7","volume":"54","author":"L.R. Scott","year":"1990","unstructured":"Scott, L.R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54, 483\u2013493 (1990)","journal-title":"Math. Comput."},{"key":"9392_CR34","volume-title":"Superconvergence Analysis and a Posteriori Error Estimation in Finite Element Methods","author":"N.N. Yan","year":"2008","unstructured":"Yan, N.N.: Superconvergence Analysis and a Posteriori Error Estimation in Finite Element Methods. Science Press, Beijing (2008)"},{"issue":"32\u201333","key":"9392_CR35","doi-asserted-by":"crossref","first-page":"4289","DOI":"10.1016\/S0045-7825(00)00319-4","volume":"190","author":"N.N. Yan","year":"2001","unstructured":"Yan, N.N., Zhou, A.H.: Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes. Comput. Methods Appl. Mech. Eng. 190(32\u201333), 4289\u20134299 (2001)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9392_CR36","first-page":"297","volume":"1","author":"N.N. Yan","year":"2008","unstructured":"Yan, N.N., Zhou, Z.J.: A priori and a posteriori error estimates of streamline diffusion finite element method for optimal control problem governed by convection dominated diffusion equation. Numer. Math.: Theory Methods Appl. 1, 297\u2013320 (2008)","journal-title":"Numer. Math.: Theory Methods Appl."},{"issue":"4","key":"9392_CR37","doi-asserted-by":"crossref","first-page":"525","DOI":"10.4208\/jcm.2009.27.4.017","volume":"27","author":"L. Yuan","year":"2009","unstructured":"Yuan, L., Yang, D.P.: A posteriori error estimate of optimal control problem of PDE with integral constraint for state. J. Comput. Math. 27(4), 525\u2013542 (2009)","journal-title":"J. Comput. Math."},{"key":"9392_CR38","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1002\/nme.1620240206","volume":"24","author":"O.C. Zienkiewicz","year":"1987","unstructured":"Zienkiewicz, O.C., Zhu, J.Z.: A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng. 24, 337\u2013357 (1987)","journal-title":"Int. J. Numer. Methods Eng."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-010-9392-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-010-9392-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-010-9392-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:41:33Z","timestamp":1559464893000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-010-9392-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,19]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["9392"],"URL":"https:\/\/doi.org\/10.1007\/s10915-010-9392-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6,19]]}}}