{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:44:00Z","timestamp":1776840240701,"version":"3.51.2"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,5,23]],"date-time":"2005-05-23T00:00:00Z","timestamp":1116806400000},"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":[[2005,6]]},"DOI":"10.1007\/s00211-004-0577-y","type":"journal-article","created":{"date-parts":[[2005,5,23]],"date-time":"2005-05-23T07:11:02Z","timestamp":1116832262000},"page":"617-637","source":"Crossref","is-referenced-by-count":63,"title":["A unifying theory of a posteriori finite element error control"],"prefix":"10.1007","volume":"100","author":[{"given":"C.","family":"Carstensen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,5,23]]},"reference":[{"key":"577_CR1","doi-asserted-by":"crossref","unstructured":"Ainsworth, M., Oden, J.T.: A posteriori error estimation in finite element analysis. Wiley-Interscience [John Wiley & Sons], New York, 2000","DOI":"10.1002\/9781118032824"},{"key":"577_CR2","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s002110050222","volume":"74","author":"Alonso","year":"4","unstructured":"Alonso, A.: Error estimators for a mixed method. Numer. Math. 74(4), 385\u2013395 (1996)","journal-title":"Numer. Math."},{"key":"577_CR3","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1137\/0726074","volume":"26","author":"Arnold","year":"1989","unstructured":"Arnold, D.N., Falk, R.S.: A uniformly accurate finite element method for the Reissner-Mindlin plate model. SIAM J. Numer. Anal. 26, 1276\u20131290 (1989)","journal-title":"SIAM J. Numer. Anal."},{"key":"577_CR4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF03167064","volume":"1","author":"Arnold","year":"2","unstructured":"Arnold, D.N., Brezzi, F., Douglas, J.: PEERS: A new finite element for plane elasticity. Japan J. Appl. Math 1(2), 347\u2013367 (1984)","journal-title":"Japan J. Appl. Math"},{"key":"577_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0045-7825(87)90114-9","volume":"61","author":"Babu\u0161ka","year":"1","unstructured":"Babu\u0161ka, I., Miller, A.: A feedback finite element method with a posteriori error estimation: Part I, The finite element method and some properties of the a posteriori estimator. Comp. Methods Appl. Mech. Engrg. 61(1), 1\u201340 (1987)","journal-title":"Comp. Methods Appl. Mech. Engrg."},{"key":"577_CR6","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1137\/0718036","volume":"18","author":"Babu\u0161ka","year":"1981","unstructured":"Babu\u0161ka, I., Rheinboldt, W.C.: A posteriori error analysis of finite element solutions for one\u2013dimensional problems SIAM J. Numer. Anal. 18, 565\u2013589 (1981)","journal-title":"Numer. Anal."},{"key":"577_CR7","doi-asserted-by":"crossref","unstructured":"Babu\u0161ka, I., Strouboulis, T.: The Finite Element Method and its Reliability. The Clarendon Press Oxford University Press, xii+802, 2001","DOI":"10.1093\/oso\/9780198502760.001.0001"},{"key":"577_CR8","first-page":"971","volume":"71","author":"Bartels","year":"239","unstructured":"Bartels, S., Carstensen, C.: Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. II. Higher order FEM. Math. Comp. 71(239), 971\u2013994 (2002)","journal-title":"II. Higher order FEM. Math. Comp."},{"key":"577_CR9","first-page":"237","volume":"4","author":"Becker","year":"1996","unstructured":"Becker, R., Rannacher, R.: A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J. Numer. Math 4, 237\u2013264 (1996)","journal-title":"East-West J. Numer. Math"},{"key":"577_CR10","doi-asserted-by":"crossref","unstructured":"Becker, R., Rannacher, R.: An optimal control approach to a posteriori error estimation in finite element methods. Acta Numerica Cambridge University Press, 2001, 1\u2013102","DOI":"10.1017\/S0962492901000010"},{"key":"577_CR11","doi-asserted-by":"crossref","unstructured":"Braess, D.: Finite Elements. Cambridge University Press, 1997","DOI":"10.1007\/978-3-662-07233-2"},{"key":"577_CR12","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s00211-003-0486-5","volume":"96","author":"Braess","year":"2004","unstructured":"Braess, D., Carstensen, C.,Reddy, B.D.: Uniform Convergence and a posteriori error estimators for the enhanced strain finite element method. Numer. Math. 96, 461\u2013479 (2004)","journal-title":"Numer. Math."},{"key":"577_CR13","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Scott, L.R.: The mathematical theory of finite element methods. Springer Verlag, New York, Texts in Applied Mathematics 15, 1994","DOI":"10.1007\/978-1-4757-4338-8"},{"key":"577_CR14","doi-asserted-by":"crossref","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991","DOI":"10.1007\/978-1-4612-3172-1"},{"key":"577_CR15","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1090\/S0025-5718-97-00837-5","volume":"66","author":"Carstensen","year":"1997","unstructured":"Carstensen, C.: A posteriori error estimate for the mixed finite element method. Math. Comp. 66, 465\u2013476 (1997)","journal-title":"Math. Comp."},{"key":"577_CR16","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s002110100378","volume":"92","author":"Carstensen","year":"2","unstructured":"Carstensen, C., Bartels, S., Dolzmann, G.: A posteriori error estimates for nonconforming finite element methods. Numer. Math. 92(2), 233\u2013256 (2002)","journal-title":"Numer. Math."},{"key":"577_CR17","unstructured":"Carstensen, C., Bartels, S., 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 (2002)"},{"key":"577_CR18","doi-asserted-by":"crossref","unstructured":"Carstensen, C., Dolzmann, G.: A posteriori error estimates for mixed FEM in elasticity. Numer. Math. 81(2) 187\u2013209 (1998)","DOI":"10.1007\/s002110050389"},{"key":"577_CR19","doi-asserted-by":"crossref","unstructured":"Carstensen, C., Dolzmann, G., Funken, S.A., Helm, D.S.: Locking-free adaptive mixed finite element methods in linear elasticity. Comput. Methods Appl. Mech. Engrg. 190(13\u201314), 1701\u20131718 (2000)","DOI":"10.1016\/S0045-7825(00)00185-7"},{"key":"577_CR20","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1090\/S0025-5718-00-01264-3","volume":"70","author":"Carstensen","year":"236","unstructured":"Carstensen, C., Funken, S.A.: A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems. Math. Comp. 70(236), 1353\u20131381 (2001)","journal-title":"Math. Comp."},{"key":"577_CR21","doi-asserted-by":"crossref","first-page":"2483","DOI":"10.1016\/S0045-7825(00)00248-6","volume":"190","author":"190","year":"2001","unstructured":"Carstensen C., Funken S.A.: Averaging technique for FE-a posteriori error control in elasticity. Part I: Conforming FEM. Comput. Methods Appl. Mech. Engrg. 190, 2483\u20132498 (2001). Part II: \u03bb-independent estimates. Comput. Methods Appl. Mech. Engrg. 190, 4663\u20134675 (2001). Part III: Locking-free conforming FEM. Comput. Methods Appl. Mech. Engrg. 191(8\u201310) 861\u2013877 (2001)","journal-title":"Part I: Conforming FEM. Comput. Methods Appl. Mech. Engrg."},{"key":"577_CR22","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1137\/S003614299732334X","volume":"36","author":"Carstensen","year":"5","unstructured":"Carstensen, C., Verf\u00fcrth, R.: Edge residuals dominate a posteriori error estimates for low order finite element methods. SIAM J. Numer. Anal. 36(5), 1571\u20131587 (1999)","journal-title":"SIAM J. Numer. Anal."},{"key":"577_CR23","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1051\/m2an\/1996300403851","volume":"30","author":"Dari","year":"4","unstructured":"Dari, E., Duran, R., Padra, C., Vampa, V.: A posteriori error estimators for nonconforming finite element methods. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 30(4), 385\u2013400 (1996)","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"577_CR24","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1090\/S0025-5718-1995-1284666-9","volume":"64","author":"Dari","year":"211","unstructured":"Dari, E., Durdfn, R., Padra, C.: Error estimators for nonconforming finite element approximations of the Stokes problem. Math. Comp. 64(211), 1017\u20131033 (1995)","journal-title":"Math. Comp."},{"key":"577_CR25","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1137\/0728003","volume":"28","author":"Eriksson","year":"1991","unstructured":"Eriksson, K., Johnson, C.: Adaptive finite element methods for parabolic problems I. A linear model problem. SIAM J. Numer. Anal. 28, 43\u201377 (1991)","journal-title":"A linear model problem. SIAM J. Numer. Anal."},{"key":"577_CR26","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1051\/m2an\/1996300202371","volume":"30","author":"Hoppe","year":"1996","unstructured":"Hoppe, R.H.W., Wohlmuth, B.: Element-orientated and edge-orientated local error estimates for nonconforming finite element methods. Math. Modeling Numer. Anal. 30, 237\u2013263 (1996)","journal-title":"Math. Modeling Numer. Anal."},{"key":"577_CR27","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0045-7825(95)00829-P","volume":"124","author":"Kouhia","year":"3","unstructured":"Kouhia, R. and Stenberg, R.: A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Engrg. 124(3), 195\u2013212 (1995)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"577_CR28","doi-asserted-by":"crossref","unstructured":"Stenberg, R.: A family of mixed finite elements for the elasticity problem. Numer. Math. 53(5) 513\u2013538 (1988)","DOI":"10.1007\/BF01397550"},{"key":"577_CR29","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF01390056","volume":"55","author":"Verf\u00fcrth","year":"3","unstructured":"Verf\u00fcrth, R.: A posteriori error estimators for the Stokes equations. Numer. Math. 55(3), 309\u2013325 (1989)","journal-title":"Numer. Math."},{"key":"577_CR30","unstructured":"Verf\u00fcrth, R.: A review of a posteriori error estimation and adaptive mesh-refinement techniques, Wiley-Teubner (1996)"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-004-0577-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-004-0577-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-004-0577-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T01:58:12Z","timestamp":1706234292000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-004-0577-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5,23]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,6]]}},"alternative-id":["577"],"URL":"https:\/\/doi.org\/10.1007\/s00211-004-0577-y","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5,23]]}}}