{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T15:10:02Z","timestamp":1719069002695},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,8,16]],"date-time":"2009-08-16T00:00:00Z","timestamp":1250380800000},"content-version":"vor","delay-in-days":227,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2009,1]]},"abstract":"We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on Q<\/jats:italic> = \u03a9<\/jats:italic> \u00d7 (0, T<\/jats:italic>], where \u03a9<\/jats:italic> is a bounded domain in \u211b<\/jats:italic>d<\/jats:italic><\/jats:sup>\u2009\u2009(d<\/jats:italic> \u2264 4) with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of our model problem in W<\/jats:italic>1,p<\/jats:italic><\/jats:sup>(\u03a9<\/jats:italic>) and L<\/jats:italic>p<\/jats:italic><\/jats:sub>(Q<\/jats:italic>) with 2 \u2264 p<\/jats:italic> < \u221e<\/jats:italic> and the almost two order superconvergence in W<\/jats:italic>1,\u221e<\/jats:italic><\/jats:sup>(\u03a9<\/jats:italic>) and L<\/jats:italic>\u221e<\/jats:italic><\/jats:sub>(Q<\/jats:italic>). Results of the p<\/jats:italic> = \u221e<\/jats:italic> case are also included in two space dimensions (d<\/jats:italic> = 1 or 2). By applying the interpolated postprocessing technique, similar results are also obtained on the error between the interpolation of the approximate solution and the exact solution.<\/jats:p>","DOI":"10.1155\/2009\/345196","type":"journal-article","created":{"date-parts":[[2009,8,16]],"date-time":"2009-08-16T15:00:16Z","timestamp":1250434816000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strong Superconvergence of Finite Element Methods for Linear Parabolic Problems"],"prefix":"10.1155","volume":"2009","author":[{"given":"Kening","family":"Wang","sequence":"first","affiliation":[]},{"given":"Shuang","family":"Li","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,8,16]]},"reference":[{"key":"e_1_2_7_1_2","series-title":"Lecture Notes in Mathematics","volume-title":"Galerkin Finite Element Methods for Parabolic Problems","author":"Thom\u00e9e V.","year":"1984"},{"key":"e_1_2_7_2_2","volume-title":"High Accuracy Theory of Finite Element Methods","author":"Chen C. M.","year":"1995"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0726033"},{"key":"e_1_2_7_4_2","unstructured":"ChenC. M. Some estimates for the nonlinear parabolic finite element Proceedings of the 1st China-Japan Joint Seminar on Numer. Math. 1992 Beijing China 87\u201390."},{"key":"e_1_2_7_5_2","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/BF02941982","article-title":"Two order superconvergence of finite element methods for Sobolev equations","volume":"8","author":"Lin Q.","year":"2001","journal-title":"The Korean Journal of Computational & Applied Mathematics"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171200002519"},{"key":"e_1_2_7_7_2","unstructured":"LinQ. YanN. N. andZhouA. N. A rectangle test for interpolated finite elements Proc. Syst. & Syst. Eng. 1991 Hong Kong Great Wall Culture 217\u2013229."},{"key":"e_1_2_7_8_2","volume-title":"The Preprocessing and Postprocessing for the Finite Element Method","author":"Lin Q.","year":"1994"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-2024(08)70178-4"},{"key":"e_1_2_7_11_2","volume-title":"Sobolev Spaces. Pure and Applied Mathematics","author":"Adams R. A.","year":"1975"},{"key":"e_1_2_7_12_2","volume-title":"Superconvergence Theory of the Finite Element Method","author":"Zhu Q. D.","year":"1989"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2009\/345196.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2009\/345196.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2009\/345196","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T14:57:51Z","timestamp":1719068271000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2009\/345196"}},"subtitle":[],"editor":[{"given":"Thomas","family":"Witelski","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1155\/2009\/345196"],"URL":"https:\/\/doi.org\/10.1155\/2009\/345196","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]},"assertion":[{"value":"2009-03-30","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-07-05","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-08-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}