{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T00:27:09Z","timestamp":1774571229197,"version":"3.50.1"},"reference-count":13,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this short note we analyse a connection between the exponentially graded and a generalisation of the class of S-type meshes for singularly perturbed problems.<\/jats:p>","DOI":"10.1515\/cmam-2017-0020","type":"journal-article","created":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T10:01:41Z","timestamp":1499335301000},"page":"199-202","source":"Crossref","is-referenced-by-count":4,"title":["A Short Note on the Connection Between Layer-Adapted Exponentially Graded and S-Type Meshes"],"prefix":"10.1515","volume":"18","author":[{"given":"Sebastian","family":"Franz","sequence":"first","affiliation":[{"name":"Institute of Scientific Computing , TU Dresden , 01062 Dresden , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christos","family":"Xenophontos","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , University of Cyprus , P.O. Box 20537, 1678 Nicosia , Cyprus"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,7,6]]},"reference":[{"key":"2023033109580931129_j_cmam-2017-0020_ref_001_w2aab3b7e1343b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"N. S.  Bakhvalov,\nThe optimization of methods of solving boundary value problems with a boundary layer,\nUSSR Comput. Math. Math. Phys. 9 (1969), no. 4, 139\u2013166.","DOI":"10.1016\/0041-5553(69)90038-X"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_002_w2aab3b7e1343b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"P.  Constantinou and C.  Xenophontos,\nFinite element analysis of an exponentially graded mesh for singularly perturbed problems,\nComput. Methods Appl. Math. 15 (2015), no. 2, 135\u2013143.","DOI":"10.1515\/cmam-2015-0002"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_003_w2aab3b7e1343b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"S.  Franz, L.  Ludwig and C.  Xenophontos,\nFinite element approximation of convection-diffusion problems using an exponentially graded mesh,\nComput. Math. Appl. 72 (2016), no. 6, 1532\u20131540.","DOI":"10.1016\/j.camwa.2016.07.008"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_004_w2aab3b7e1343b1b6b1ab2ab4Aa","unstructured":"S.  Franz, L.  Ludwig and C.  Xenophontos,\nFinite element approximation of reaction-diffusion problems using an exponentially graded mesh,\nin preparation."},{"key":"2023033109580931129_j_cmam-2017-0020_ref_005_w2aab3b7e1343b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"T.  Lin\u00df,\nAnalysis of a Galerkin finite element method on a Bakhvalov\u2013Shishkin mesh for a linear convection-diffusion problem,\nIMA J. Numer. Anal. 20 (2000), no. 4, 621\u2013632.","DOI":"10.1093\/imanum\/20.4.621"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_006_w2aab3b7e1343b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"T.  Lin\u00df,\nLayer-Adapted Meshes for Reaction-Convection-Diffusion Problems,\nLecture Notes in Math. 1985,\nSpringer, Berlin, 2010.","DOI":"10.1007\/978-3-642-05134-0"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_007_w2aab3b7e1343b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"H.-G.  Roos and T.  Lin\u00df,\nSufficient conditions for uniform convergence on layer-adapted grids,\nComputing 63 (1999), 27\u201345.","DOI":"10.1007\/s006070050049"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_008_w2aab3b7e1343b1b6b1ab2ab8Aa","unstructured":"H.-G.  Roos, M.  Stynes and L.  Tobiska,\nRobust Numerical Methods for Singularly Perturbed Differential Equations, 2nd ed.,\nSpringer Ser. Comput. Math. 24,\nSpringer, Berlin, 2008."},{"key":"2023033109580931129_j_cmam-2017-0020_ref_009_w2aab3b7e1343b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"H.-G.  Roos, L.  Teofanov and Z.  Uzelac,\nGraded meshes for high order FEM,\nJ. Comput. Math. 33 (2015), no. 1, 1\u201316.","DOI":"10.4208\/jcm.1405-m4362"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_010_w2aab3b7e1343b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"G.  Shishkin,\nGrid approximation of singularly perturbed elliptic and parabolic equations (in Russian),\nSecond doctorial thesis, Keldysh Institute, Moscow, 1990.","DOI":"10.1515\/rnam.1989.4.1.69"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_011_w2aab3b7e1343b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"M.  van Veldhuizen,\nHigher order methods for a singularly perturbed problem,\nNumer. Math. 30 (1978), 267\u2013279.","DOI":"10.1007\/BF01411843"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_012_w2aab3b7e1343b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"C.  Xenophontos,\nOptimal mesh design for the finite element approximation of reaction-diffusion problems,\nInternat. J. Numer. Methods Engrg. 53 (2002), 929\u2013943.","DOI":"10.1002\/nme.318"},{"key":"2023033109580931129_j_cmam-2017-0020_ref_013_w2aab3b7e1343b1b6b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"C.  Xenophontos,\nA parameter robust finite element method for fourth order singularly perturbed problems,\nComput. Methods Appl. Math. 17 (2017), no. 2, 337\u2013349.","DOI":"10.1515\/cmam-2016-0045"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/18\/2\/article-p199.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0020\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0020\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T10:32:50Z","timestamp":1680258770000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0020\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,6]]},"references-count":13,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,6,7]]},"published-print":{"date-parts":[[2018,4,1]]}},"alternative-id":["10.1515\/cmam-2017-0020"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2017-0020","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2017,7,6]]}}}