{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:10:18Z","timestamp":1758402618069,"version":"3.41.2"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,11,26]],"date-time":"2012-11-26T00:00:00Z","timestamp":1353888000000},"content-version":"vor","delay-in-days":330,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10971203","11126132"],"award-info":[{"award-number":["10971203","11126132"]}],"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":["10971203","11126132"],"award-info":[{"award-number":["10971203","11126132"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper studies the finite element (FE) approximation to a second\u2010type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming EQ<jats:sup>rot<\/jats:sup> FE schemes under a reasonable regularity of the exact solution <jats:italic>u<\/jats:italic> \u2208 <jats:italic>H<\/jats:italic><jats:sup>5\/2<\/jats:sup>(\u03a9), which seem to be never discovered in the previous literature. The optimal <jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>\u2010norm error estimate is also derived for EQ<jats:sup>rot<\/jats:sup> FE. At last, some numerical results are provided to verify the theoretical analysis.<\/jats:p>","DOI":"10.1155\/2012\/156095","type":"journal-article","created":{"date-parts":[[2012,11,26]],"date-time":"2012-11-26T21:08:00Z","timestamp":1353964080000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Superconvergence Analysis of Finite Element Method for a Second\u2010Type Variational Inequality"],"prefix":"10.1155","volume":"2012","author":[{"given":"Dongyang","family":"Shi","sequence":"first","affiliation":[]},{"given":"Hongbo","family":"Guan","sequence":"additional","affiliation":[]},{"given":"Xiaofei","family":"Guan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,11,26]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392210"},{"key":"e_1_2_7_2_2","unstructured":"StrangG. 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