{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:57:42Z","timestamp":1776869862394,"version":"3.51.2"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"233","license":[{"start":{"date-parts":[[2001,10,2]],"date-time":"2001-10-02T00:00:00Z","timestamp":1001980800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The use of finite elements in smooth domains leads naturally to polyhedral or piecewise polynomial approximations of the boundary. Hence the approximation error consists of two parts: the geometric part and the finite element part. We propose to exploit this decomposition in the error analysis by introducing an auxiliary problem defined in a polygonal domain approximating the original smooth domain. The finite element part of the error can be treated in the standard way. To estimate the geometric part of the error, we need quantitative estimates related to perturbation of the geometry. We derive such estimates using the techniques developed for shape sensitivity analysis.<\/p>","DOI":"10.1090\/s0025-5718-00-01323-5","type":"journal-article","created":{"date-parts":[[2005,7,11]],"date-time":"2005-07-11T17:02:26Z","timestamp":1121101346000},"page":"1-15","source":"Crossref","is-referenced-by-count":6,"title":["Shape calculus and finite element method in smooth domains"],"prefix":"10.1090","volume":"70","author":[{"given":"T.","family":"Tiihonen","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,10,2]]},"reference":[{"key":"1","first-page":"76","article-title":"Stabilit\u00e4t des Definitionsgebietes mit R\u00fccksicht auf grundlegende Probleme der Theorie der partiellen Differentialgleichungen auch im Zusammenhang mit der Elastizit\u00e4tstheorie. I, II","volume":"11(86)","author":"Babu\u0161ka, Ivo","year":"1961","journal-title":"Czechoslovak Math. 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