{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:30:07Z","timestamp":1787232607167,"version":"build-2736575974"},"reference-count":6,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. and Stat. Comput."],"published-print":{"date-parts":[[1990,3]]},"abstract":"<jats:p>A class of finite-element methods for elliptic problems is shown to exhibit nodal superconvergence in the approximate solution, and some equivalence properties to familiar finite-difference operators are demonstrated. The superconvergence property is exploited in a Taylor series analysis to demonstrate Gauss-point superconvergence for the derivatives of the approximation. A post-processing formula for the derivative at the nodes is constructed and shown to exhibit superconvergence. The nodal superconvergence property can be exploited recursively to further enhance the finite-element or finite-difference solution. Supporting numerical studies are given.<\/jats:p>","DOI":"10.1137\/0911020","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:36:55Z","timestamp":1109648215000},"page":"343-353","source":"Crossref","is-referenced-by-count":23,"title":["Nodal Superconvergence and Solution Enhancement for a Class of Finite-Element and Finite-Difference Methods"],"prefix":"10.1137","volume":"11","author":[{"given":"R. J.","family":"MacKinnon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G. F.","family":"Carey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","first-page":"399","volume":"3","author":"Bramble J. H.","year":"1964","journal-title":"Contributions to Differential Equations"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(82)90029-9"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(85)90085-4"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0713032"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90104-0"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0711062"}],"container-title":["SIAM Journal on Scientific and Statistical Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0911020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:08:02Z","timestamp":1787231282000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0911020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["10.1137\/0911020"],"URL":"https:\/\/doi.org\/10.1137\/0911020","relation":{},"ISSN":["0196-5204","2168-3417"],"issn-type":[{"value":"0196-5204","type":"print"},{"value":"2168-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}