{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T00:27:10Z","timestamp":1774571230315,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present the mathematical analysis for the convergence of an <jats:italic>h<\/jats:italic> version\nFinite Element Method (FEM) with piecewise polynomials of degree <jats:italic>p<\/jats:italic> \u2265 1,\ndefined on an <jats:italic>exponentially graded<\/jats:italic> mesh. The analysis is presented\nfor a singularly perturbed reaction-diffusion and a\nconvection-diffusion equation in one dimension. We prove convergence of optimal order and\nindependent of the singular perturbation parameter, when the error is measured in the natural\nenergy norm associated with each problem. Numerical results comparing the\nexponential mesh with the Bakhvalov\u2013Shishkin mesh from the literature are\nalso presented.<\/jats:p>","DOI":"10.1515\/cmam-2015-0002","type":"journal-article","created":{"date-parts":[[2015,2,17]],"date-time":"2015-02-17T17:01:21Z","timestamp":1424192481000},"page":"135-143","source":"Crossref","is-referenced-by-count":31,"title":["Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems"],"prefix":"10.1515","volume":"15","author":[{"given":"Philippos","family":"Constantinou","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus"}]},{"given":"Christos","family":"Xenophontos","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus"}]}],"member":"374","published-online":{"date-parts":[[2015,2,17]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/15\/2\/article-p135.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0002\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0002\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:39:56Z","timestamp":1680302396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0002\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,3,10]]},"published-print":{"date-parts":[[2015,4,1]]}},"alternative-id":["10.1515\/cmam-2015-0002"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0002","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,17]]}}}