{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:17:32Z","timestamp":1773249452572,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,9,13]],"date-time":"2012-09-13T00:00:00Z","timestamp":1347494400000},"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":[[2013,3]]},"DOI":"10.1007\/s00211-012-0494-4","type":"journal-article","created":{"date-parts":[[2012,9,12]],"date-time":"2012-09-12T08:47:16Z","timestamp":1347439636000},"page":"425-459","source":"Crossref","is-referenced-by-count":13,"title":["Effective postprocessing for equilibration a posteriori error estimators"],"prefix":"10.1007","volume":"123","author":[{"given":"C.","family":"Carstensen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Merdon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,9,13]]},"reference":[{"key":"494_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032824","volume-title":"A Posteriori Error Estimation in Finite Element Analysis","author":"M Ainsworth","year":"2000","unstructured":"Ainsworth, M., Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. Wiley, New York (2000)"},{"issue":"2","key":"494_CR2","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s00211-004-0553-6","volume":"99","author":"S Bartels","year":"2004","unstructured":"Bartels, S., Carstensen, C.: Averaging techniques yield reliable a posteriori finite element error control for obstacle problems. Numer. Math. 99(2), 225\u2013249 (2004)","journal-title":"Numer. Math."},{"issue":"1","key":"494_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00211-004-0548-3","volume":"99","author":"S Bartels","year":"2004","unstructured":"Bartels, S., Carstensen, C., Dolzmann, G.: Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. Numer. Math. 99(1), 1\u201324 (2004)","journal-title":"Numer. Math."},{"issue":"1\u20134","key":"494_CR4","first-page":"79","volume":"15","author":"S Bartels","year":"2001","unstructured":"Bartels, S., Carstensen, C., Klose, R.: An experimental survey of a posteriori Courant finite element error control for the Poisson equation. Adv. Comput. Math. 15(1\u20134), 79\u2013106 (2001)","journal-title":"Adv. Comput. Math."},{"key":"494_CR5","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s00211-005-0634-1","volume":"101","author":"D Braess","year":"2005","unstructured":"Braess, D.: A posteriori error estimators for obstacle problems\u2014another look. Numer. Math. 101, 415\u2013421 (2005)","journal-title":"Numer. Math."},{"key":"494_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511618635","volume-title":"Finite Elements\u2014Theory, Fast Solvers, and Applications in Solid Mechanics","author":"D Braess","year":"2007","unstructured":"Braess, D.: Finite Elements\u2014Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, New York (2007)"},{"key":"494_CR7","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502760.001.0001","volume-title":"The Finite Element Method and Its Reliability. Numerical Mathematics and Scientific Computation","author":"I Babu\u0161ka","year":"2001","unstructured":"Babu\u0161ka, I., Strouboulis, T.: The Finite Element Method and Its Reliability. Numerical Mathematics and Scientific Computation. The Clarendon Press Oxford University Press, New York (2001)"},{"issue":"262","key":"494_CR8","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1090\/S0025-5718-07-02080-7","volume":"77","author":"D Braess","year":"2008","unstructured":"Braess, D., Sch\u00f6berl, J.: Equilibrated residual error estimator for edge elements. Math. Comp. 77(262), 651\u2013672 (2008)","journal-title":"Math. Comp."},{"key":"494_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The Mathematical Theory of Finite Element Methods, 3rd edn","author":"SC Brenner","year":"2008","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, 3rd edn. Springer, New York (2008)"},{"issue":"4","key":"494_CR10","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1007\/s00211-004-0577-y","volume":"100","author":"C Carstensen","year":"2005","unstructured":"Carstensen, C.: A unifying theory of a posteriori finite element error control. Numer. Math. 100(4), 617\u2013637 (2005)","journal-title":"Numer. Math."},{"key":"494_CR11","doi-asserted-by":"crossref","unstructured":"Carstensen, C., Eigel, M., Hoppe, R.H.W., L\u00f6bhard, C.: A Review of Unified A Posteriori Finite Element Error Control. Numer. Math. Theor. Meth. Appl. 5(4), 509\u2013558 (2010). doi: 10.4208\/nmtma.2011.m1032","DOI":"10.4208\/nmtma.2011.m1032"},{"issue":"3","key":"494_CR12","doi-asserted-by":"crossref","first-page":"309","DOI":"10.4208\/jcm.2009.10-m1015","volume":"28","author":"C Carstensen","year":"2010","unstructured":"Carstensen, C., Merdon, C.: Estimator competition for Poisson problems. J. Comput. Math. 28(3), 309\u2013330 (2010)","journal-title":"J. Comput. Math."},{"key":"494_CR13","doi-asserted-by":"crossref","unstructured":"Carstensen, C., Merdon, C.: A posteriori error estimator competition for conforming obstacle problems. Numer. Methods Partial Differ. Equ. (2012). doi: 10.1002\/num.21728","DOI":"10.1002\/num.21728"},{"key":"494_CR14","doi-asserted-by":"crossref","unstructured":"Carstensen, C., Merdon, C.: Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem (2012, submitted)","DOI":"10.1016\/j.cam.2012.12.021"},{"key":"494_CR15","unstructured":"Carstensen, C., Peterseim, D., Schedensack, M.: Comparison results of three first-order finite element methods for the poisson model problem. SIAM J. Numer. Anal. http:\/\/opus4.kobv.de\/opus4-matheon\/frontdoor\/index\/index\/docId\/940 (2012, preprint)"},{"key":"494_CR16","doi-asserted-by":"crossref","unstructured":"Girault, V., Raviart, P.A.: Finite element methods for Navier Stokes equations. Springer-Verlag, Berlin (1986)","DOI":"10.1007\/978-3-642-61623-5"},{"key":"494_CR17","volume-title":"A Posteriori Error Analysis Via Duality Theory. Advances in Mechanics and Mathematics","author":"W Han","year":"2005","unstructured":"Han, W.: A Posteriori Error Analysis Via Duality Theory. Advances in Mechanics and Mathematics. Springer, New York (2005)"},{"key":"494_CR18","unstructured":"Hoppe, R.H.W., Wohlmuth, B.: Element-oriented and edge-oriented local error estimators for nonconforming finite element methods. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 30(2), 237\u2013263 (1996). MR 1382112 (97e:65124)"},{"issue":"4","key":"494_CR19","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.1137\/S0036142903433790","volume":"42","author":"R Luce","year":"2004","unstructured":"Luce, R., Wohlmuth, B.I.: A local a posteriori error estimator based on equilibrated fluxes. SIAM J. Numer. Anal. 42(4), 1394\u20131414 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"494_CR20","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1137\/0722029","volume":"22","author":"LD Marini","year":"1985","unstructured":"Marini, L.D.: An inexpensive method for the evaluation of the solution of the lowest order Raviart\u2013Thomas mixed method. SIAM J. Numer. Anal. 22, 493\u2013496 (1985)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"494_CR21","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1137\/060675666","volume":"47","author":"MS Mommer","year":"2009","unstructured":"Mommer, M.S., Stevenson, R.: A goal-oriented adaptive finite element method with convergence rates. SIAM J. Numer. Anal. 47(2), 861\u2013886 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"494_CR22","unstructured":"Prager, W., Synge, J. L.: Approximations in elasticity based on the concept of function space. Quart. Appl. Math. 5, 241\u2013269 (1947). MR 0025902 (10,81b)"},{"key":"494_CR23","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1007\/BF00252910","volume":"5","author":"LE Payne","year":"1960","unstructured":"Payne, L.E., Weinberger, H.F.: An optimal Poincar\u00e9 inequality for convex domains. Arch. Rat. Mech. Anal. 5, 286\u2013292 (1960)","journal-title":"Arch. Rat. Mech. Anal."},{"key":"494_CR24","unstructured":"Repin, S.I.: Two-sided estimates of deviation from exact solutions of uniformly elliptic equations. In: Proceedings of the St. Petersburg Mathematical Society, Vol. IX (Providence, RI), American Mathematical Society. Translations: Series 2, vol. 209. American Mathematical Society, pp. 143\u2013171 (2003). MR 2018375 (2004k:35081)"},{"key":"494_CR25","doi-asserted-by":"crossref","DOI":"10.1515\/9783110203042","volume-title":"A Posteriori Estimates for Partial Differential Equations. Radon Series on Computational and Applied Mathematics","author":"S Repin","year":"2008","unstructured":"Repin, S.: A Posteriori Estimates for Partial Differential Equations. Radon Series on Computational and Applied Mathematics. Walter de Gruyter, Berlin (2008)"},{"issue":"3","key":"494_CR26","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s00607-003-0013-7","volume":"70","author":"S Repin","year":"2003","unstructured":"Repin, S., Sauter, S., Smolianski, A.: A posteriori error estimation for the Dirichlet problem with account of the error in the approximation of boundary conditions. Computing 70(3), 205\u2013233 (2003)","journal-title":"Computing"},{"key":"494_CR27","doi-asserted-by":"crossref","unstructured":"Valdman, J.: Minimization of functional majorant in a posteriori error analysis based on H(div) multigrid-preconditioned CG method. Adv. Numer. Anal. (2009). Art ID 164519, MR 2739760 (2011j:65290)","DOI":"10.1155\/2009\/164519"},{"key":"494_CR28","volume-title":"A Review of A-Posteriori Error Estimation and Adaptive Mesh Refinement Techniques","author":"R Verf\u00fcrth","year":"1996","unstructured":"Verf\u00fcrth, R.: A Review of A-Posteriori Error Estimation and Adaptive Mesh Refinement Techniques. Wiley-Teubner, Amsterdam (1996)"},{"issue":"3","key":"494_CR29","doi-asserted-by":"crossref","first-page":"2387","DOI":"10.1137\/080738283","volume":"47","author":"A Veeser","year":"2009","unstructured":"Veeser, A., Verf\u00fcrth, R.: Explicit upper bounds for dual norms of residuals. SIAM J. Numer. Anal. 47(3), 2387\u20132405 (2009)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-012-0494-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-012-0494-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-012-0494-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T04:52:45Z","timestamp":1714366365000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-012-0494-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,13]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["494"],"URL":"https:\/\/doi.org\/10.1007\/s00211-012-0494-4","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9,13]]}}}