{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T21:05:30Z","timestamp":1778792730676,"version":"3.51.4"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,1,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>\n\t\t\t\t\t\tThe local discontinuous Galerkin method (LDG) is considered for\n\t\t\t\t\t\tsolving one-dimensional singularly perturbed two-point boundary\n\t\t\t\t\t\tvalue problems of reaction-diffusion type. Pointwise error\n\t\t\t\t\t\testimates for the LDG approximation to the solution and its\n\t\t\t\t\t\tderivative are established on a Shishkin-type mesh. Numerical\n\t\t\t\t\t\texperiments are presented. Moreover, a superconvergence of order <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2012-0004_8e1708cdb5f141d403c40a81a45f2fbb.png\"\/> of the numerical traces is observed numerically.\n\t\t\t\t\t<\/jats:p>","DOI":"10.1515\/cmam-2012-0004","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T16:01:19Z","timestamp":1380297679000},"page":"79-94","source":"Crossref","is-referenced-by-count":9,"title":["Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems"],"prefix":"10.1515","volume":"13","author":[{"given":"Huiqing","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhimin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, MI 48202, USA; and Beijing Computational Science Research Center, No.\u00a03 Heqing Road, Haidian District, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2013,1,3]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/1\/article-p79.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2012-0004\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2012-0004\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:38Z","timestamp":1614481418000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2012-0004\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,3]]},"published-print":{"date-parts":[[2013,1,1]]}},"alternative-id":["10.1515\/cmam-2012-0004"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2012-0004","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}