{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:07:14Z","timestamp":1760267234649},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,7,16]],"date-time":"2013-07-16T00:00:00Z","timestamp":1373932800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2014,4]]},"DOI":"10.1007\/s10444-013-9313-4","type":"journal-article","created":{"date-parts":[[2013,7,15]],"date-time":"2013-07-15T11:59:59Z","timestamp":1373889599000},"page":"399-413","source":"Crossref","is-referenced-by-count":10,"title":["Superconvergence of finite volume element method for elliptic problems"],"prefix":"10.1007","volume":"40","author":[{"given":"Tie","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,7,16]]},"reference":[{"key":"9313_CR1","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1137\/0724050","volume":"24","author":"RE Bank","year":"1987","unstructured":"Bank, R.E., Rose, D.J.: Some error estimates for the box method. SIAM J. Numer. Anal. 24, 777\u2013787 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"9313_CR2","first-page":"713","volume":"58","author":"ZQ Cai","year":"1991","unstructured":"Cai, Z.Q.: On the finite volume element method. Numer. Math. 58, 713\u2013735 (1991)","journal-title":"Numer. Math."},{"key":"9313_CR3","first-page":"22","volume":"33","author":"ZY Chen","year":"1994","unstructured":"Chen, Z.Y.: L 2 estimate of linear element generalized difference schemes. Acta. Sci. Nat. Univ. Sunyatseni 33, 22\u201328 (1994)","journal-title":"Acta. Sci. Nat. Univ. Sunyatseni"},{"key":"9313_CR4","first-page":"163","volume":"3","author":"ZY Chen","year":"1994","unstructured":"Chen, Z.Y.: Superconvergence of generalized difference methods for elliptic boundary value problem. Numer. Math. A J. Chinese Univ. (English Ser) 3, 163\u2013171 (1994)","journal-title":"Numer. Math. A J. Chinese Univ. (English Ser)"},{"key":"9313_CR5","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1023\/A:1014577215948","volume":"16","author":"ZY Chen","year":"2002","unstructured":"Chen, Z.Y., Li, R.H., Zhou, A.H.: A note on the optimal L 2-estimate of the finite volume element method. Adv. Comput. Math. 16, 291\u2013303 (2002)","journal-title":"Adv. Comput. Math."},{"key":"9313_CR6","doi-asserted-by":"crossref","first-page":"4021","DOI":"10.1137\/080720164","volume":"47","author":"L Chen","year":"2010","unstructured":"Chen, L.: A new class of high order finite volume element methods for second order elliptic equations. SIAM J. Numer. Anal. 47, 4021\u20134023 (2010)","journal-title":"SIAM J. Numer. Anal."},{"key":"9313_CR7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1090\/S0025-5718-99-01192-8","volume":"69","author":"S.H Chou","year":"2000","unstructured":"Chou, S.H., Li, Q.: Error estimates in L 2, H 1, L \u221e in covolume methods for elliptic and parabolic problem: a unified approach. Math. Comput. 69, 103\u2013120 (2000)","journal-title":"Math. Comput."},{"key":"9313_CR8","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.1016\/j.cma.2006.10.025","volume":"196","author":"SH Chou","year":"2007","unstructured":"Chou, S.H., Ye, X.: Superconvergence of finite volume methods for the second order elliptic problem. Comput. Methods Appl. Mech. Eng. 196, 3706\u20133712 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9313_CR9","doi-asserted-by":"crossref","first-page":"1865","DOI":"10.1137\/S0036142900368873","volume":"39","author":"RE Ewing","year":"2002","unstructured":"Ewing, R.E., Lin, T., Lin, Y.P.: On the accuracy of the finite volume element method based on piecewise linear polynomials. SIAM J. Numer. Anal. 39, 1865\u20131888 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9313_CR10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1137\/0733003","volume":"33","author":"R Lazarov","year":"1996","unstructured":"Lazarov, R., Michev, I., Vassilevski, P.: Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33, 31\u201355 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"9313_CR11","first-page":"140","volume":"4","author":"RH Li","year":"1982","unstructured":"Li, R.H., Zhu, P.Q.: Generalized difference methods for second order elliptic partial differentil equations I. The case of a triangular mesh. Numer. Math. A J Chinese Univ. 4, 140\u2013152 (1982)","journal-title":"Numer. Math. A J Chinese Univ."},{"key":"9313_CR12","volume-title":"Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods","author":"RH Li","year":"2000","unstructured":"Li, R.H., Chen, Z.Y., Wu, W.: Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods. Marcel, New York (2000)"},{"key":"9313_CR13","volume-title":"The Preprocessing and Postprocessing for the Finite Element Methods","author":"Q Lin","year":"1994","unstructured":"Lin, Q., Zhu, Q.D.: The Preprocessing and Postprocessing for the Finite Element Methods. Shanghai Sci & Tech Publishing, Shanghai (1994)"},{"key":"9313_CR14","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s10444-011-9215-2","volume":"37","author":"JL Lv","year":"2012","unstructured":"Lv, J.L., Li, Y.H.: L 2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes. Adv. Comput. Math. 37, 393\u2013416 (2012)","journal-title":"Adv. Comput. Math."},{"key":"9313_CR15","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/BF02238536","volume":"51","author":"T Schmidt","year":"1993","unstructured":"Schmidt, T.: Box schemes on quadrilateral meshes. Computing 51, 271\u2013292 (1993)","journal-title":"Computing"},{"key":"9313_CR16","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1137\/0728073","volume":"28","author":"E S\u00fcli","year":"1991","unstructured":"S\u00fcli, E.: Convergence of finite volume schemes for poission\u2019s equation on nonuniform meshes. SIAM J. Numer. Anal. 28, 1419\u20131430 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"9313_CR17","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1002\/num.10068","volume":"19","author":"HJ Wu","year":"2003","unstructured":"Wu, H.J., Li, R.H.: Error estimate for finite volume element methods for general second order elliptic problem. Numer. Methods Partial Differential Equations 19, 693\u2013708 (2003)","journal-title":"Numer. Methods Partial Differential Equations"},{"key":"9313_CR18","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s00211-008-0189-z","volume":"111","author":"JC Xu","year":"2009","unstructured":"Xu, J.C., Zou, Q.S.: Analysis of linear and quadratic simplical finite volume methods for elliptic equations. Numer. Math. 111, 469\u2013492 (2009)","journal-title":"Numer. Math."},{"key":"9313_CR19","volume-title":"Finite Element Methods for Evolution Integro-Differential Equations","author":"T Zhang","year":"2001","unstructured":"Zhang, T.: Finite Element Methods for Evolution Integro-Differential Equations. Northeastern Univ Publishing House, Shenyang (2001)"},{"key":"9313_CR20","first-page":"491","volume":"20","author":"T Zhang","year":"2002","unstructured":"Zhang, T., Lin, Y.P., Tait, R.J.: On the finite volume element version of Ritz-Volterra projection and applications to related equations. J. Comput. Math. 20, 491\u2013504 (2002)","journal-title":"J. Comput. Math."},{"key":"9313_CR21","volume-title":"The Superconvergence Theory of Finite Elements","author":"QD Zhu","year":"1989","unstructured":"Zhu, Q.D., Lin, Q.: The Superconvergence Theory of Finite Elements. Hunan Science and Technology Publishing House, Changsha (1989)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9313-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-013-9313-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9313-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T13:08:18Z","timestamp":1559135298000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-013-9313-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,16]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,4]]}},"alternative-id":["9313"],"URL":"https:\/\/doi.org\/10.1007\/s10444-013-9313-4","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,16]]}}}