{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T07:17:08Z","timestamp":1784618228527,"version":"3.55.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"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":["11571384"],"award-info":[{"award-number":["11571384"]}],"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":["11428103"],"award-info":[{"award-number":["11428103"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1419040"],"award-info":[{"award-number":["1419040"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471031"],"award-info":[{"award-number":["11471031"]}],"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":["91430216"],"award-info":[{"award-number":["91430216"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,3]]},"DOI":"10.1007\/s10915-017-0501-0","type":"journal-article","created":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T10:15:28Z","timestamp":1500545728000},"page":"1397-1422","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["A $$C^0$$ Linear Finite Element Method for Biharmonic Problems"],"prefix":"10.1007","volume":"74","author":[{"given":"Hailong","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhimin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingsong","family":"Zou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,7,20]]},"reference":[{"key":"501_CR1","unstructured":"Adini, A., Clough, R.W.: Analysis of plate bending by the finite element method, NSF report G. 7337 (1961)"},{"key":"501_CR2","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824","volume-title":"A Posteriori Error Estimation in Finite Element Analysis","author":"M Ainsworth","year":"2000","unstructured":"Ainsworth, M., Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. Wiley Interscience, New York (2000)"},{"key":"501_CR3","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502760.001.0001","volume-title":"The Finite Element Method and Its Reliability","author":"I Babuska","year":"2001","unstructured":"Babuska, I., Strouboulis, T.: The Finite Element Method and Its Reliability. Oxford University Press, London (2001)"},{"key":"501_CR4","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1090\/S0025-5718-1985-0777265-X","volume":"44","author":"RE Bank","year":"1985","unstructured":"Bank, R.E., Weiser, A.: Some a posteriori error estimators for elliptic partial differential equations. Math. comp. 44, 283\u2013301 (1985)","journal-title":"Math. comp."},{"key":"501_CR5","doi-asserted-by":"publisher","first-page":"2294","DOI":"10.1137\/S003614290139874X","volume":"41","author":"RE Bank","year":"2003","unstructured":"Bank, R.E., Xu, J.: Asymptotically exact a posteriori error estimators, Part I: Grid with superconvergence. SIAM J. Numer. Anal. 41, 2294\u20132312 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"501_CR6","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1090\/S0025-5718-1977-0431742-5","volume":"31","author":"GA Baker","year":"1977","unstructured":"Baker, G.A.: Fintie element methods for elliptic equations using nonconforming elements. Math. Comp. 31, 45\u201359 (1977)","journal-title":"Math. Comp."},{"key":"501_CR7","doi-asserted-by":"publisher","first-page":"2313","DOI":"10.1137\/S0036142901398751","volume":"41","author":"RE Bank","year":"2003","unstructured":"Bank, R.E., Xu, J.: Asymptotically exact a posteriori error estimators, Part II: general unstructured grids. SIAM J. Numer. Anal. 41, 2313\u20132332 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"501_CR8","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s10915-004-4135-7","volume":"22\/23","author":"S Brenner","year":"2005","unstructured":"Brenner, S., Sung, L.: C0 interior penalty methods for fourth order elliptic boundary value problems on polygonal domains. J. Sci. Comput. 22\/23, 83\u2013118 (2005)","journal-title":"J. Sci. Comput."},{"key":"501_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"Mathematical Theory of Finite element Methods","author":"S Brenner","year":"2008","unstructured":"Brenner, S., Scott, L.R.: Mathematical Theory of Finite element Methods, 3rd edn. Spriger-Verlag, New York (2008)","edition":"3"},{"key":"501_CR10","volume-title":"The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications","author":"PG Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications, vol. 4. North-Holland, Amsterdam (1978)"},{"key":"501_CR11","unstructured":"COMSOL Multiphysics 3.5a User\u2019s Guide, p. 471 (2008)"},{"key":"501_CR12","unstructured":"Introduction to COMSOL Multiphysics Version 5.1, p. 46 (2015)"},{"key":"501_CR13","volume-title":"Spectral Approximation of Linear Operators, Computer Science and Applied Mathematics","author":"Francoise Chatelin","year":"1983","unstructured":"Chatelin, Francoise: Spectral Approximation of Linear Operators, Computer Science and Applied Mathematics. Academic Press Inc., New York (1983)"},{"key":"501_CR14","doi-asserted-by":"publisher","unstructured":"Chen, H., Guo, H., Zhang, Z., Zou, Q.: A $$C^0$$ Linear Finite Element Method For Two Fourth-Order Eigenvalue Problems IMA. J. Numer. Anal. (2016). doi: 10.1093\/imanum\/drw051","DOI":"10.1093\/imanum\/drw051"},{"key":"501_CR15","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.cam.2016.03.003","volume":"307","author":"H Guo","year":"2016","unstructured":"Guo, H., Zhang, Z., Zhao, R., Zou, Q.: Polynomial preserving recovery on boundary. J. Comput. Appl. Math. 307, 119\u2013133 (2016)","journal-title":"J. Comput. Appl. Math."},{"key":"501_CR16","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1007\/s10915-016-0312-8","volume":"71","author":"H Guo","year":"2017","unstructured":"Guo, H., Yang, X.: Polynomial preserving recovery for high frequency wave propagation. J. Sci. Comput. 71, 594\u2013614 (2017)","journal-title":"J. Sci. Comput."},{"key":"501_CR17","doi-asserted-by":"publisher","first-page":"920","DOI":"10.4236\/am.2012.38137","volume":"3","author":"M El-Gamel","year":"2012","unstructured":"El-Gamel, M., Sameeh, M.: An efficient technique for finding the eigenvalues of fourth-order Sturm\u2013Liouville problems. Appl. Math. 3, 920\u2013925 (2012)","journal-title":"Appl. Math."},{"key":"501_CR18","doi-asserted-by":"publisher","first-page":"5188","DOI":"10.1016\/j.cam.2011.05.005","volume":"235","author":"B Lamichhane","year":"2011","unstructured":"Lamichhane, B.: A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems. J. Comput. Appl. Math. 235, 5188\u20135197 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"501_CR19","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1007\/s10543-013-0462-0","volume":"54","author":"B Lamichhane","year":"2014","unstructured":"Lamichhane, B.: A finite element method for a biharmonic equation based on gradient recovery operators. BIT Numer. Math. 54, 469\u2013484 (2014)","journal-title":"BIT Numer. Math."},{"key":"501_CR20","first-page":"239","volume":"586","author":"H Li","year":"2013","unstructured":"Li, H., Nistor, V.: LNG_FEM: graded meshes on domains of polygonal structures. Rec. Adv. Sci. Comput. Appl. 586, 239\u2013246 (2013)","journal-title":"Rec. Adv. Sci. Comput. Appl."},{"key":"501_CR21","doi-asserted-by":"crossref","first-page":"149C","DOI":"10.1017\/S0001925900004546","volume":"19","author":"L Morley","year":"1968","unstructured":"Morley, L.: The triangular equilibrium problem in the solution of plate bending problems. Aero. Quart. 19, 149C\u2013169 (1968)","journal-title":"Aero. Quart."},{"key":"501_CR22","doi-asserted-by":"publisher","first-page":"1780","DOI":"10.1137\/S0036142903413002","volume":"42\u20134","author":"A Naga","year":"2004","unstructured":"Naga, A., Zhang, Z.: A posteriori error estimates based on the polynomial preserving recovery. SIAM J. Numer. Anal. 42\u20134, 1780\u20131800 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"501_CR23","first-page":"769","volume":"5\u20133","author":"A Naga","year":"2005","unstructured":"Naga, A., Zhang, Z.: The polynomial-preserving recovery for higher order finite element methods in 2D and 3D. Discret. Contin. Dyn. Syst.-Ser. B 5\u20133, 769\u2013798 (2005)","journal-title":"Discret. Contin. Dyn. Syst.-Ser. B"},{"key":"501_CR24","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1137\/100797709","volume":"50","author":"A Naga","year":"2012","unstructured":"Naga, A., Zhang, Z.: Function value recovery and its application in eigenvalue problems. SIAM J. Numer. Anal. 50, 272\u2013286 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"501_CR25","unstructured":"Niceno, B.: EasyMesh Version 1.4: A two-dimensional quality mesh generator. http:\/\/www-dinma.univ.trieste.it\/nirftc\/research\/easymesh"},{"key":"501_CR26","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s00211-006-0685-y","volume":"103","author":"M Wang","year":"2006","unstructured":"Wang, M., Xu, J.: The Morley element for fourth order elliptic equations in any dimensions. Numer. Math. 103, 155\u2013169 (2006)","journal-title":"Numer. Math."},{"key":"501_CR27","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1090\/S0025-5718-03-01600-4","volume":"73","author":"J Xu","year":"2004","unstructured":"Xu, J., Zhang, Z.: Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comp. 73, 1139\u20131152 (2004)","journal-title":"Math. Comp."},{"key":"501_CR28","first-page":"73","volume":"5","author":"S Zhang","year":"2008","unstructured":"Zhang, S., Zhang, Z.: Invalidity of decoupling a biharmonic equation to two Poisson equations on non-convex polygons. Int. J. Numer. Anal. Model. 5, 73\u201376 (2008)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"501_CR29","first-page":"333","volume-title":"Adaptive Computations: Theory and Algorithms. Mathematics Monograph Series 6","author":"Z Zhang","year":"2007","unstructured":"Zhang, Z.: Recovery Techniques in Finite Element Methods. In: Tang, T., Xu, J. (eds.) Adaptive Computations: Theory and Algorithms. Mathematics Monograph Series 6, pp. 333\u2013412. Science Publisher, London (2007)"},{"key":"501_CR30","doi-asserted-by":"publisher","first-page":"1192","DOI":"10.1137\/S1064827503402837","volume":"26\u20134","author":"Z Zhang","year":"2005","unstructured":"Zhang, Z., Naga, A.: A new finite element gradient recovery method: superconvergence property. SIAM J. Sci. Comput. 26\u20134, 1192\u20131213 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"501_CR31","doi-asserted-by":"publisher","first-page":"1331","DOI":"10.1002\/nme.1620330702","volume":"33","author":"OC Zienkiewicz","year":"1992","unstructured":"Zienkiewicz, O.C., Zhu, J.Z.: The superconvergence patch recovery and a posteriori error estimates part 1: the recovery technique. Int. J. Numer. Methods Eng. 33, 1331\u20131364 (1992)","journal-title":"Int. J. Numer. Methods Eng."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0501-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0501-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0501-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T16:42:04Z","timestamp":1750783324000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0501-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,20]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["501"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0501-0","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,20]]},"assertion":[{"value":"8 December 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 June 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2017","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2017","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}