{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:01:20Z","timestamp":1759838480457,"version":"3.41.0"},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the<jats:italic>h<\/jats:italic>version of the finite element method. In particular, we use piecewise Hermite polynomials of degree<jats:inline-formula id=\"j_cmam-2016-0045_ineq_9999_w2aab3b7e2495b1b6b1aab1c13b1b3Aa\"><jats:alternatives><m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><m:mrow><m:mi>p<\/m:mi><m:mo>\u2265<\/m:mo><m:mn>3<\/m:mn><\/m:mrow><\/m:math><jats:tex-math>${p\\geq 3}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>defined on an<jats:italic>exponentially graded<\/jats:italic>mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, \u2018balanced\u2019 norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.<\/jats:p>","DOI":"10.1515\/cmam-2016-0045","type":"journal-article","created":{"date-parts":[[2017,1,10]],"date-time":"2017-01-10T10:01:27Z","timestamp":1484042487000},"page":"337-349","source":"Crossref","is-referenced-by-count":6,"title":["A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems"],"prefix":"10.1515","volume":"17","author":[{"given":"Christos","family":"Xenophontos","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus"}]}],"member":"374","published-online":{"date-parts":[[2017,1,10]]},"reference":[{"key":"2024051216151932326_j_cmam-2016-0045_ref_001_w2aab3b7e2495b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Allen III M. B. and Isaacson E. 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