{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T23:47:24Z","timestamp":1784072844463,"version":"3.55.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,1,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nWe consider the stationary reaction-diffusion problem in a domain\n<jats:inline-formula id=\"eq1_w2aab2b8c18b1b7b1aab1c12b1b1Aa\"><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2013-0024_58eeeec0907b5bf0dd725e8eccc6a760.png\"\/><jats:tex-math>$\\Omega \\subset \\mathbb {R}^3$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> having the size along\none coordinate direction essentially smaller than along the others. By an energy type argumentation, different simplified models of lower dimension can be deduced and solved numerically.\nFor these models, we derive a guaranteed upper bound of the difference between the exact solution of the original problem and a three-dimensional reconstruction generated by the solution of a dimensionally reduced problem. This estimate of the total error is determined as the sum of discretization and modeling errors, which are both explicit and computable. The corresponding discretization errors are estimated by a posteriori estimates of the functional type. Modeling error majorants are also explicitly evaluated. Hence, a numerical strategy based on the balancing modeling and discretization errors can be derived in order to provide an economical way of getting an approximate solution with an a priori given accuracy. Numerical tests are presented and discussed.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0024","type":"journal-article","created":{"date-parts":[[2014,1,9]],"date-time":"2014-01-09T20:13:43Z","timestamp":1389298423000},"page":"113-134","source":"Crossref","is-referenced-by-count":4,"title":["Combined Error Estimates in the Case of Dimension Reduction"],"prefix":"10.1515","volume":"14","author":[{"given":"Tatiana","family":"Samrowski","sequence":"first","affiliation":[{"name":"1School of Engineering, Zurich University of Applied Sciences, Technikumstrasse 9, 8401 Winterthur, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/1\/article-p113.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/14\/1\/article-p113.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:47Z","timestamp":1614481427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0024\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0024","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}