{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:37:48Z","timestamp":1776836268761,"version":"3.51.2"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2005,6,13]],"date-time":"2005-06-13T00:00:00Z","timestamp":1118620800000},"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":[[2005,8]]},"DOI":"10.1007\/s00211-005-0616-3","type":"journal-article","created":{"date-parts":[[2005,6,12]],"date-time":"2005-06-12T05:49:17Z","timestamp":1118555357000},"page":"309-332","source":"Crossref","is-referenced-by-count":13,"title":["A posteriori dual-mixed adaptive finite element error control for Lam\u00e9 and Stokes equations"],"prefix":"10.1007","volume":"101","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paola","family":"Causin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Sacco","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,13]]},"reference":[{"key":"616_CR1","doi-asserted-by":"crossref","unstructured":"Arnold, D.N., Brezzi, F.: Mixed and nonconforming finite element methods: Implementation postprocessing and error estimates. Math. Modeling Numer. Anal. 19-1, 7\u201332 (1985)","DOI":"10.1051\/m2an\/1985190100071"},{"key":"616_CR2","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF03167064","volume":"1","author":"Arnold","year":"1984","unstructured":"Arnold, D.N., Brezzi, F., Douglas, J.: PEERS: A new mixed finite element for plane elasticity. Japan J. Appl. Math. 1, 347\u2013367 (1984)","journal-title":"Japan J. Appl. Math."},{"key":"616_CR3","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01395876","volume":"53","author":"Arnold","year":"1988","unstructured":"Arnold, D.N., Falk, R.: A new mixed formulation for elasticity. Numer. Math. 53, 13\u201330 (1988)","journal-title":"Numer. Math."},{"key":"616_CR4","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1137\/0728033","volume":"28","author":"Bank","year":"1991","unstructured":"Bank, R.E., Welfert, B.D.: A posteriori error estimates for the Stokes problem. SIAM J. Numer. Anal. 28, 591\u2013623 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"616_CR5","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s002110100337","volume":"91","author":"Barrientos","year":"2","unstructured":"Barrientos, M.A., Gatica, G.N., Stephan, E.P.: A mixed finite method for nonlinear elasticity: Two-fold saddle point approach and a-posteriori error estimate. Numer. Math. 91(2), 197\u2013222 (2002)","journal-title":"Numer. Math."},{"key":"616_CR6","unstructured":"Braess, D.: Finite elements. Cambridge University Press, Cambridge, 2001"},{"key":"616_CR7","first-page":"461","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 Numer. Math. 96, 461\u2013479 (2004)","journal-title":"Math."},{"key":"616_CR8","doi-asserted-by":"crossref","unstructured":"Brenner, S., Carstensen, C.: Finite element methods. Encyclopedia of Computational Mechanics, 2004 (in press)","DOI":"10.1002\/0470091355.ecm003"},{"key":"616_CR9","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":"616_CR10","doi-asserted-by":"crossref","unstructured":"Carstensen, C.: A unifying theory of a posteriori finite element error control. 2005. Numer. Math. accepted for publication","DOI":"10.1007\/s00211-004-0577-y"},{"key":"616_CR11","first-page":"187","volume":"81","author":"Carstensen","year":"1998","unstructured":"Carstensen, C., Dolzmann, G.: A posteriori error estimates for mixed FEM in elasticity Numer. Math. 81, 187\u2013209 (1998)","journal-title":"Math."},{"key":"616_CR12","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1016\/S0045-7825(00)00185-7","volume":"190","author":"Carstensen","year":"2000","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, 1701\u20131718 (2000)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"616_CR13","first-page":"2483","volume":"190","author":"Carstensen","year":"2001","unstructured":"Carstensen, C., Funken, S.: Averaging technique for FE-a posteriori error control in elasticity. Part I: Conforming FEM Part II: \u03bb-independent estimates Part III: Locking-free nonconforming FEM. Comput. Methods Appl. Mech. Engrg. 190, 2483\u20132498 (2001)","journal-title":"Part I: Conforming FEM Part II: \u03bb-independent estimates Part III: Locking-free nonconforming FEM. Comput. Methods Appl. Mech. Engrg."},{"key":"616_CR14","doi-asserted-by":"crossref","unstructured":"Carstensen, C., Funken, S.: A posteriori error control in low order finite element discretizations of incompressible stationary flow problems. Math. Comp. 70\u2013236, 1353\u20131381 (2001)","DOI":"10.1090\/S0025-5718-00-01264-3"},{"key":"616_CR15","unstructured":"Causin, P.: Mixed-hybrid Galerkin and Petrov-Galerkin finite element formulations in fluid mechanics. Universit\u00e0 degli Studi di Milano, 2002"},{"key":"616_CR16","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/S0045-7825(02)00574-1","volume":"192","author":"Causin","year":"2003","unstructured":"Causin, P., Sacco, R.: A dual-mixed hybrid formulation for fluid mechanics problems: mathematical analysis and application to semiconductor process technology. Comput. Methods Appl. Mech. Engrg. 192, 593\u2013612 (2003)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"616_CR17","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.G.: The finite element method for elliptic problems. North Holland, Amsterdam, 1978","DOI":"10.1115\/1.3424474"},{"key":"616_CR18","unstructured":"Cockburn, B., Gopalakrishnan, J.: Error analysis of variable degree mixed methods for elliptic problems via hybridization. To appear in Math. Comp."},{"key":"616_CR19","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1137\/S0036142902417893","volume":"42","author":"Cockburn","year":"2004","unstructured":"Cockburn, B., Gopalakrishnan, J.: A characterization of hybridized mixed methods for the Dirichlet problem. SIAM J. Numer. Anal. 42, 283\u2013301 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"616_CR20","doi-asserted-by":"crossref","unstructured":"Eriksson, K., Estep, D., Hansbo, P., Johnson, C.: Introduction to adaptive methods for differential equations. Acta Numerica, 1995, pp 105\u2013158","DOI":"10.1017\/S0962492900002531"},{"key":"616_CR21","doi-asserted-by":"crossref","unstructured":"Farhloul, M., Fortin, M.: Dual hybrid methods for the elasticity and the Stokes problems: a unified approach. Numer. Math. 76\u20134, 419\u2013440 (1997)","DOI":"10.1007\/s002110050270"},{"key":"616_CR22","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/1099-1476(200102)24:3<179::AID-MMA204>3.0.CO;2-M","volume":"24","author":"Gatica","year":"3","unstructured":"Gatica, G.N., Heuer, N., Stephan, E.P.: An implicit-explicit residual error estimator for the coupling of dual-mixed finite elementsand boundary elements in elastostatics. Math. Meth. in Appl. Sciences 24(3), 179\u2013191 (2001)","journal-title":"Math. Meth. in Appl. Sciences"},{"key":"616_CR23","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1002\/num.1046","volume":"18","author":"Gatica","year":"1","unstructured":"Gatica, G.N., Stephan, E.P.: A mixed-fem formulation for nonlinear incompressible elasticity in the plane. Numer. Meth. Part. Diff. Eqtns. 18(1), 105\u2013128 (2002)","journal-title":"Numer. Meth. Part. Diff. Eqtns."},{"key":"616_CR24","unstructured":"Grisvard, P.: Singularities in elasticity theory. In: P.G. Ciarlet, E. Sanchez-Palencia (eds.), Applications of multiple scaling in Mechanics, pp 134\u2013150. Masson, Paris, 1987"},{"key":"616_CR25","doi-asserted-by":"crossref","unstructured":"Herrmann, L.R.: Elasticity equations for incompressible and nearly-incompressible materials by a variational theorem. AIAA Jnl. 3\u201310, 1896\u20131900 (1965)","DOI":"10.2514\/3.3277"},{"key":"616_CR26","unstructured":"Hughes, T.J.R.: The Finite element method linear static and dynamic analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1987"},{"key":"616_CR27","doi-asserted-by":"crossref","unstructured":"Raviart, P.A., Thomas, J.M.: A mixed finite element method for second order elliptic problems. In: I. Galligani, E. Magenes (eds.), Mathematical Aspects of Finite Element Methods, I. Springer-Verlag, Berlin, 1977","DOI":"10.1007\/BFb0064470"},{"key":"616_CR28","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF01390056","volume":"55","author":"Verf\u00fcrth","year":"1989","unstructured":"Verf\u00fcrth, R.: A posteriori error estimator for the stokes equations. Numer. Math. 55, 309\u2013325 (1989)","journal-title":"Numer. Math."},{"key":"616_CR29","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/BF01385723","volume":"60","author":"Verf\u00fcrth","year":"1991","unstructured":"Verf\u00fcrth, R.: A posteriori error estimator for the stokes equations. II: Nonconforming discretizations. Numer. Math. 60, 235\u2013249 (1991)","journal-title":"II: Nonconforming discretizations. Numer. Math."},{"key":"616_CR30","doi-asserted-by":"crossref","unstructured":"Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Meth. Appl. Mech. Eng. 101(1\u20133), 207\u2013224 (1992)","DOI":"10.1016\/0045-7825(92)90023-D"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0616-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-005-0616-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0616-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T17:30:40Z","timestamp":1586280640000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-005-0616-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6,13]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2005,8]]}},"alternative-id":["616"],"URL":"https:\/\/doi.org\/10.1007\/s00211-005-0616-3","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6,13]]}}}