{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:31Z","timestamp":1740123931420,"version":"3.37.3"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T00:00:00Z","timestamp":1563926400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T00:00:00Z","timestamp":1563926400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11826212"],"award-info":[{"award-number":["11826212"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671341"],"award-info":[{"award-number":["11671341"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009377","name":"Education Department of Hunan Province","doi-asserted-by":"publisher","award":["16A206"],"award-info":[{"award-number":["16A206"]}],"id":[{"id":"10.13039\/100009377","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002767","name":"Hunan Provincial Science and Technology Department","doi-asserted-by":"publisher","award":["2018WK4006"],"award-info":[{"award-number":["2018WK4006"]}],"id":[{"id":"10.13039\/501100002767","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2019JJ20016"],"award-info":[{"award-number":["2019JJ20016"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s10444-019-09714-9","type":"journal-article","created":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T10:55:57Z","timestamp":1563965757000},"page":"2833-2844","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Superconvergence of the Crouzeix-Raviart element for elliptic equation"],"prefix":"10.1007","volume":"45","author":[{"given":"Yidan","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Yunqing","family":"Huang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2106-8237","authenticated-orcid":false,"given":"Nianyu","family":"Yi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,7,24]]},"reference":[{"key":"9714_CR1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502760.001.0001","volume-title":"The Finite Element Method and Its Reliability","author":"I Babu\u0161ka","year":"2001","unstructured":"Babu\u0161ka, I., Strouboulis, T.: The Finite Element Method and Its Reliability. Clarendon Press, New York (2001)"},{"key":"9714_CR2","doi-asserted-by":"publisher","first-page":"2294","DOI":"10.1137\/S003614290139874X","volume":"41","author":"RE Bank","year":"2003","unstructured":"Bank, R.E., Xu, J.C.: Asymptotically exact a posteriori error estimators, part I: grids with superconvergence. SIAM J. Numer. Anal. 41, 2294\u20132312 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"9714_CR3","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s002110050064","volume":"68","author":"JH Brandts","year":"1994","unstructured":"Brandts, J.H.: Superconvergence and a posteriori error estimation for triangular mixed finite elements. Numer. Math. 68, 311\u2013324 (1994)","journal-title":"Numer. Math."},{"key":"9714_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics","author":"F Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics. Springer, New York (1991)"},{"key":"9714_CR5","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1007\/s10915-017-0377-z","volume":"72","author":"W Cao","year":"2017","unstructured":"Cao, W., Huang, Q.: Superconvergence of local discontinuous Galerkin methods for partial differential equations with higher order derivatives. J Sci. Comput. 72, 761\u2013791 (2017)","journal-title":"J Sci. Comput."},{"key":"9714_CR6","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1002\/num.22087","volume":"33","author":"W Cao","year":"2017","unstructured":"Cao, W., Liu, H., Zhang, Z.: Superconvergence of the direct discontinuous Galerkin method for convection\u2013diffusion equations. Numer. Methods Partial Differ. Eq. 33, 290\u2013317 (2017)","journal-title":"Numer. Methods Partial Differ. Eq."},{"key":"9714_CR7","first-page":"12","volume":"2","author":"C Chen","year":"1980","unstructured":"Chen, C.: Optimal points of the stresses for triangular linear element (in Chinese). Numer. Math. J. Chinese Univ. 2, 12\u201320 (1980)","journal-title":"Numer. Math. J. Chinese Univ."},{"key":"9714_CR8","first-page":"118","volume":"3","author":"C Chen","year":"1981","unstructured":"Chen, C.: Superconvergence of finite element solutions and their derivatives (in Chinese). Numer. Math. J. Chinese Univ. 3, 118\u2013125 (1981)","journal-title":"Numer. Math. J. Chinese Univ."},{"key":"9714_CR9","volume-title":"Structure Theory of Superconvergence of Finite Elements (in Chinese)","author":"C Chen","year":"2002","unstructured":"Chen, C.: Structure Theory of Superconvergence of Finite Elements (in Chinese). Hunan Science and Technology Press, Changsha (2002)"},{"key":"9714_CR10","volume-title":"High Accuracy Theory of Finite Element Methods (in Chinese)","author":"C Chen","year":"1995","unstructured":"Chen, C., Huang, Y.: High Accuracy Theory of Finite Element Methods (in Chinese). Hunan Science Press, Hunan (1995)"},{"key":"9714_CR11","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s002110050084","volume":"69","author":"H Chen","year":"1994","unstructured":"Chen, H., Li, B.: Superconvergence analysis and error expansion for the Wilson nonconforming finite element. Numer. Math. 69, 125\u2013140 (1994)","journal-title":"Numer. Math."},{"key":"9714_CR12","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.: The Finite Element Method for Elliptic Problems. North-Holland (1978)","DOI":"10.1115\/1.3424474"},{"key":"9714_CR13","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/S0036142900371544","volume":"39","author":"B Cockburn","year":"2002","unstructured":"Cockburn, B., Kanschat, G., Perugia, I., Sch\u00f6tzau, D.: Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. SIAM J. Numer. Anal. 39, 264\u2013285 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9714_CR14","first-page":"33","volume":"7","author":"M Crouzeix","year":"1973","unstructured":"Crouzeix, M., Raviart, P.A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations I. RAIRO Anal Numer. 7, 33\u201375 (1973)","journal-title":"RAIRO Anal Numer."},{"key":"9714_CR15","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1090\/S0025-5718-1985-0771029-9","volume":"44","author":"J Douglas","year":"1985","unstructured":"Douglas, J., Roberts, J.E.: Global estimates for mixed methods for 2 nd order elliptic problems. Math. Comp. 44, 39\u201352 (1985)","journal-title":"Math. Comp."},{"key":"9714_CR16","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/BF02575724","volume":"26","author":"J Douglas","year":"1989","unstructured":"Douglas, J., Wang, J.: Superconvergence of mixed finite element methods on rectangular domains. Calcolo 26, 121\u2013134 (1989)","journal-title":"Calcolo"},{"key":"9714_CR17","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1007\/BF01385626","volume":"58","author":"R Duran","year":"1990","unstructured":"Duran, R.: Superconvergence for rectangular mixed finite elements. Numer. Math. 58, 2\u201315 (1990)","journal-title":"Numer. Math."},{"key":"9714_CR18","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1137\/0728054","volume":"28","author":"RE Ewing","year":"1991","unstructured":"Ewing, R.E., Lazarov, R.D., Wang, J.: Superconvergence of the velocity along the Gauss lines in mixed finite element methods. SIAM J. Numer. Anal. 28, 1015\u20131029 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"9714_CR19","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s00211-015-0729-2","volume":"132","author":"J Hu","year":"2016","unstructured":"Hu, J., Ma, R.: Superconvergence of both the Crouzeix-Raviart and Morley elements. Numer. Math. 132, 491\u2013509 (2016)","journal-title":"Numer. Math."},{"key":"9714_CR20","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1201\/9780203756034-13","volume-title":"finite element methods","author":"Yun-Qing Huang","year":"2017","unstructured":"Huang, Y.: The superconvergence of finite element methods on domains with reentrant corners. In: Finite Element Methods: Superconvergence, Post-Processing, and a Posteriori Estimates, pp. 169\u2013182. Marcel Dekker, Inc., New York (1998)"},{"key":"9714_CR21","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1090\/S0025-5718-08-02051-6","volume":"77","author":"Y Huang","year":"2008","unstructured":"Huang, Y., Xu, J.: Superconvergence of quadratic finite elements on mildly structured grids. Math. Comp. 77, 1253\u20131268 (2008)","journal-title":"Math. Comp."},{"key":"9714_CR22","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BFb0076087","volume":"1192","author":"M K\u0159i\u017eek","year":"1986","unstructured":"K\u0159i\u017eek, M.: Superconvergence results for linear triangular elements. Lect. Notes Math. Springer 1192, 315\u2013320 (1986)","journal-title":"Lect. Notes Math. Springer"},{"key":"9714_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0045-7825(99)00281-9","volume":"189","author":"AM Lakhany","year":"2000","unstructured":"Lakhany, A.M., Marek, I., Whiteman, J.R.: Superconvergence results in mildly structured triangulations. Comput. Methods Appl. Mech. Engry. 189, 1\u201375 (2000)","journal-title":"Comput. Methods Appl. Mech. Engry."},{"key":"9714_CR24","doi-asserted-by":"publisher","first-page":"792","DOI":"10.1137\/17M112587X","volume":"56","author":"Y Li","year":"2018","unstructured":"Li, Y: Superconvergence of the lowest order mixed finite element on mildly structured meshes. SIAM J. Numer. Anal. 56, 792\u2013815 (2018)","journal-title":"SIAM J. Numer. Anal."},{"key":"9714_CR25","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1093\/imanum\/drh008","volume":"25","author":"Q Lin","year":"2005","unstructured":"Lin, Q., Tobiska, L., Zhou, A.: On the superconvergence of nonconforming low order finite elements applied to the Poisson equation. IMA J. Numer. Anal. 25, 160\u2013181 (2005)","journal-title":"IMA J. Numer. Anal."},{"key":"9714_CR26","first-page":"115","volume":"3","author":"Q Lin","year":"1985","unstructured":"Lin, Q., Xu, J.: Linear finite elements with high accuracy. J. Comput. Math. 3, 115\u2013133 (1985)","journal-title":"J. Comput. Math."},{"key":"9714_CR27","volume-title":"The Construction and Analysis of High Efficiency Finite Elements (in Chinese)","author":"Q Lin","year":"1996","unstructured":"Lin, Q., Yan, N.: The Construction and Analysis of High Efficiency Finite Elements (in Chinese). Hebei University Press, Hebei (1996)"},{"key":"9714_CR28","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/s00211-008-0190-6","volume":"111","author":"S Mao","year":"2009","unstructured":"Mao, S., Shi, Z.: High accuracy analysis of two nonconforming plate elements. Numer. Math. 111, 407\u2013443 (2009)","journal-title":"Numer. Math."},{"key":"9714_CR29","doi-asserted-by":"publisher","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-Thomas mixed method. SIAM J. Numer. Anal. 22, 493\u2013496 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"9714_CR30","first-page":"477","volume":"606","author":"PA Raviart","year":"1977","unstructured":"Raviart, P.A., Thomas, J.M.: A mixed finite element method for second order elliptic problems. Lect. Notes Math. 606, 477\u2013503 (1977)","journal-title":"Lect. Notes Math."},{"key":"9714_CR31","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s002110050312","volume":"78","author":"Z Shi","year":"1997","unstructured":"Shi, Z., Jiang, B.: A new superconvergence property of Wilson nonconforming finite element. Numer. Math. 78, 259\u2013268 (1997)","journal-title":"Numer. Math."},{"key":"9714_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0096835","volume-title":"Superconvergence in Galkerkin Finite Element Methods","author":"LB Wahlbin","year":"1995","unstructured":"Wahlbin, L.B.: Superconvergence in Galkerkin Finite Element Methods. Springer Verlag, Berlin (1995)"},{"key":"9714_CR33","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1002\/num.1036","volume":"18","author":"X Ye","year":"2002","unstructured":"Ye, X.: Superconvergence of nonconforming fnite element method for the Stokes equations. Numer. Methods Partial Differ. Eq. 18, 143\u2013154 (2002)","journal-title":"Numer. Methods Partial Differ. Eq."},{"key":"9714_CR34","doi-asserted-by":"publisher","first-page":"663","DOI":"10.2307\/2006479","volume":"32","author":"M Zl\u00e1mal","year":"1978","unstructured":"Zl\u00e1mal, M.: Superconvergence and reduced integration in the finite element method. Math. Comp. 32, 663\u2013685 (1978)","journal-title":"Math. Comp."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09714-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-019-09714-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09714-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,21]],"date-time":"2024-07-21T08:53:43Z","timestamp":1721552023000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-019-09714-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,24]]},"references-count":34,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["9714"],"URL":"https:\/\/doi.org\/10.1007\/s10444-019-09714-9","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2019,7,24]]},"assertion":[{"value":"14 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 July 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}