{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T04:22:24Z","timestamp":1777090944655,"version":"3.51.4"},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,10,17]],"date-time":"2009-10-17T00:00:00Z","timestamp":1255737600000},"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>\n                    We analyze a semidiscrete numerical scheme for approximating the evolution of parametric curves by elastic flow in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R Superscript n\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {R}^n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The fourth order equation is split into two coupled second order problems, which are approximated by linear finite elements. We prove error bounds for the resulting scheme and present numerical test calculations that confirm our analysis.\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02176-5","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"645-671","source":"Crossref","is-referenced-by-count":38,"title":["Error analysis for the elastic flow of parametrized curves"],"prefix":"10.1090","volume":"78","author":[{"given":"Klaus","family":"Deckelnick","sequence":"first","affiliation":[]},{"given":"Gerhard","family":"Dziuk","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,10,17]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/j.jcp.2006.07.026","article-title":"A parametric finite element method for fourth order geometric evolution equations","volume":"222","author":"Barrett, John W.","year":"2007","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"21","DOI":"10.4171\/IFB\/134","article-title":"Error analysis of a finite element method for the Willmore flow of graphs","volume":"8","author":"Deckelnick, Klaus","year":"2006","journal-title":"Interfaces Free Bound.","ISSN":"https:\/\/id.crossref.org\/issn\/1463-9963","issn-type":"print"},{"key":"3","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1017\/S0962492904000224","article-title":"Computation of geometric partial differential equations and mean curvature flow","volume":"14","author":"Deckelnick, Klaus","year":"2005","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"key":"4","unstructured":"G. Dziuk, Computational parametric Willmore flow, Preprint Fakult\u00e4t f\u00fcr Mathematik und Physik 07\u201313 (2007)."},{"issue":"5","key":"5","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1137\/S0036141001383709","article-title":"Evolution of elastic curves in \u211d\u207f: existence and computation","volume":"33","author":"Dziuk, Gerhard","year":"2002","journal-title":"SIAM J. Math. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1410","issn-type":"print"},{"key":"6","unstructured":"A. Polden, Curves and surfaces of least total curvature and fourth\u2013order flows, Ph.D. dissertation, Universit\u00e4t T\u00fcbingen, T\u00fcbingen, Germany, 1996."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02176-5\/S0025-5718-08-02176-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02176-5\/S0025-5718-08-02176-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:56:36Z","timestamp":1776786996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02176-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,10,17]]},"references-count":6,"journal-issue":{"issue":"266","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0025-5718-08-02176-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-08-02176-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2008,10,17]]}}}