{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:18:03Z","timestamp":1776845883202,"version":"3.51.2"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,11,27]],"date-time":"2007-11-27T00:00:00Z","timestamp":1196121600000},"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":[[2008,1]]},"DOI":"10.1007\/s00211-007-0121-y","type":"journal-article","created":{"date-parts":[[2007,11,26]],"date-time":"2007-11-26T11:39:04Z","timestamp":1196077144000},"page":"487-500","source":"Crossref","is-referenced-by-count":47,"title":["A posteriori error estimates for mixed finite element approximations of elliptic problems"],"prefix":"10.1007","volume":"108","author":[{"given":"Mats G.","family":"Larson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Axel","family":"M\u00e5lqvist","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,11,27]]},"reference":[{"key":"121_CR1","unstructured":"Adams, R.A.: Sobolev spaces. Pure and Applied Mathematics, vol. 65. Academic, New York (1975)"},{"key":"121_CR2","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1051\/m2an\/1985190100071","volume":"19","author":"D.N. Arnold","year":"1985","unstructured":"Arnold D.N. and Brezzi F. (1985). Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 19: 7\u201332","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"121_CR3","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/S0045-7825(02)00593-5","volume":"192","author":"R. Becker","year":"2003","unstructured":"Becker R., Hansbo P. and Larson M.G. (2003). Energy norm a posteriori error estimation for discontinuous Galerkin methods. Comput. Methods Appl. Mech. Eng. 192: 723\u2013733","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"121_CR4","doi-asserted-by":"crossref","first-page":"2431","DOI":"10.1137\/S0036142994264079","volume":"33","author":"D. Braess","year":"1996","unstructured":"Braess D. and Verf\u00fcrt R. (1996). A posteriori error estimators for the Raviart\u2013Thomas element. SIAM J. Numer. Anal. 33: 2431\u20132444","journal-title":"SIAM J. Numer. Anal."},{"key":"121_CR5","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1137\/0726073","volume":"26","author":"J.H. Bramble","year":"1989","unstructured":"Bramble J.H. and Xu J. (1989). A local post-processing technique for improving the accuracy in mixed finite-element approximations. SIAM J. Numer. Anal. 26: 1267\u20131275","journal-title":"SIAM J. Numer. Anal."},{"key":"121_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4338-8","volume-title":"The Mathematical Theory of Finite Element Methods","author":"S.C. Brenner","year":"1994","unstructured":"Brenner S.C. and Scott L.R. (1994). The Mathematical Theory of Finite Element Methods. Springer, Heidelberg"},{"key":"121_CR7","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF01396752","volume":"51","author":"F. Brezzi","year":"1987","unstructured":"Brezzi F., Dur\u00e1n R., Fortin M. and Douglas J. Jr (1987). Mixed finite elements for second order elliptic problems in three variables. Numer. Math. 51: 237\u2013250","journal-title":"Numer. Math."},{"key":"121_CR8","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF01389710","volume":"47","author":"F. Brezzi","year":"1985","unstructured":"Brezzi F., Marini D.L. and Douglas J. (1985). Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47: 217\u2013235","journal-title":"Numer. Math."},{"key":"121_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods","author":"F. Brezzi","year":"1991","unstructured":"Brezzi F. and Fortin M. (1991). Mixed and Hybrid Finite Element Methods. Springer, Heidelberg"},{"key":"121_CR10","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1090\/S0025-5718-97-00837-5","volume":"66","author":"C. Carstensen","year":"1997","unstructured":"Carstensen C. (1997). A posteriori error estimate for the mixed finite element method. Math. Comp. 66: 465\u2013476","journal-title":"Math. Comp."},{"key":"121_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0063447","volume-title":"Finite Element Approximation of the Navier\u2013Stokes Equation","author":"V. Girault","year":"1979","unstructured":"Girault V. and Raviart P.-A. (1979). Finite Element Approximation of the Navier\u2013Stokes Equation. Springer, Berlin"},{"key":"121_CR12","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1090\/S0025-5718-06-01872-2","volume":"75","author":"C. Lovadina","year":"2006","unstructured":"Lovadina C. and Stenberg R. (2006). Energy norm a posteriori error estimates for mixed finite element methods. Math. Comp. 75: 1659\u20131674","journal-title":"Math. Comp."},{"key":"121_CR13","doi-asserted-by":"crossref","first-page":"4341","DOI":"10.1016\/S0045-7825(02)00371-7","volume":"191","author":"A. Masud","year":"2002","unstructured":"Masud A. and Hughes T.J.R. (2002). A stabilized finite element method for Darcy flow. Comput. Methods Appl. Mech. Eng. 191: 4341\u20134370","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"121_CR14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF01389668","volume":"50","author":"J.-C. N\u00e9d\u00e9lec","year":"1986","unstructured":"N\u00e9d\u00e9lec J.-C. (1986). A new family of mixed finite elements in R 3. Numer. Math. 50: 57\u201381","journal-title":"Numer. Math."},{"key":"121_CR15","doi-asserted-by":"crossref","unstructured":"Raviart, P., Thomas, J.: A mixed finite element method for second order elliptic problems. In: Mathematical aspects of the finite element method. Lecture Notes in Math, vol. 606, pp. 292\u2013315. Springer, Heidelberg (1977)","DOI":"10.1007\/BFb0064470"},{"key":"121_CR16","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1007\/BF01405291","volume":"56","author":"R. Stenberg","year":"1990","unstructured":"Stenberg R. (1990). Some new families of finite elements for the Stokes equations. Numer. Math. 56: 827\u2013838","journal-title":"Numer. Math."},{"key":"121_CR17","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1051\/m2an\/1991250101511","volume":"25","author":"R. Stenberg","year":"1991","unstructured":"Stenberg R. (1991). Postprocessing schemes for some mixed finite elements. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 25: 151\u2013167","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"121_CR18","doi-asserted-by":"crossref","unstructured":"Roberts, J.E., Thomas, J.-M.: Mixed and hybrid methods. Ciarlet, P.G., Lions, J.L. (eds) Handbook of Numerical Analysis. Finite Element Methods (Part 1), vol. II, pp. 523\u2013639. Elsevier, Amsterdam (1991)","DOI":"10.1016\/S1570-8659(05)80041-9"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0121-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-007-0121-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0121-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:22:40Z","timestamp":1558628560000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-007-0121-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,27]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["121"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0121-y","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,27]]}}}