{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T02:11:38Z","timestamp":1648519898233},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,7,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nWe study the convergence of finite difference schemes for approximating\nelliptic equations of second order with discontinuous coefficients.\nTwo of these finite difference schemes arise from the discretization\nby the finite element method using bilinear shape functions.\nWe prove\nan <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2013-0012_56170d86f4d9bf5f96a9871c0efe9829.png\" \/> convergence for the gradient, if the solution is locally in <jats:italic>H<jats:sup>3<\/jats:sup><\/jats:italic>. Thus, in contrast to the first order convergence\nfor the gradient obtained by the finite element theory we show that the gradient is superclose.\nFrom the Bramble\u2013Hilbert Lemma we derive a higher order compact (HOC) difference scheme\nthat gives an approximation error of order four for the gradient.\nA numerical example is given.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0012","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T16:01:19Z","timestamp":1380297679000},"page":"281-289","source":"Crossref","is-referenced-by-count":0,"title":["On Finite Difference Schemes for Elliptic Equations with Discontinuous Coefficients"],"prefix":"10.1515","volume":"13","author":[{"given":"Manfred","family":"Dobrowolski","sequence":"first","affiliation":[{"name":"1Faculty of Mathematics and Informatics, University of W\u00fcrzburg, Emil-Fischer-Str.\u00a030, 97074 W\u00fcrzburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/3\/article-p281.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/3\/article-p281.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:43Z","timestamp":1614481423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0012\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,1]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0012","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,1]]}}}