{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T03:35:52Z","timestamp":1777520152533,"version":"3.51.4"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,4,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>\nA functional type a posteriori error estimator for the finite element discretization of the stationary reaction-convection-diffusion equation is derived.\nIn case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients.\nThis renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial.\nFunctional error estimators as derived here contain no mesh-dependent constants and provide guaranteed error bounds for any conforming approximation.\nTo evaluate the error estimator, a minimization problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space.\nBased on a set of numerical examples, we assess the performance of the new estimator.\nIt is observed that it exhibits a good efficiency also with convection-dominated problem settings.\n<\/jats:p>","DOI":"10.1515\/cmam-2014-0005","type":"journal-article","created":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T20:10:44Z","timestamp":1394655044000},"page":"135-150","source":"Crossref","is-referenced-by-count":3,"title":["Functional A Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems"],"prefix":"10.1515","volume":"14","author":[{"given":"Martin","family":"Eigel","sequence":"first","affiliation":[{"name":"Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tatiana","family":"Samrowski","sequence":"additional","affiliation":[{"name":"Zurich University of Applied Sciences, Technikumstrasse 9, 8400 Winterthur, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,3,13]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/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-2014-0005\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0005\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:32:25Z","timestamp":1680298345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0005\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,13]]},"published-print":{"date-parts":[[2014,4,1]]}},"alternative-id":["10.1515\/cmam-2014-0005"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2014-0005","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,13]]}}}