We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of the bending energy and the tangent-point functional.<\/p>\n
Based on estimates for the second derivative of the latter and a uniform bi-Lipschitz radius, we prove a stability result implying energy decay during the evolution as well as maintenance of arclength parametrization.<\/p>\n
Finally we present some numerical experiments exploring the energy landscape, targeted to the question how to obtain global minimizers of the bending energy in knot classes, so-called elastic knots.<\/p>","DOI":"10.1090\/mcom\/3633","type":"journal-article","created":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T11:23:09Z","timestamp":1612351389000},"page":"1499-1526","source":"Crossref","is-referenced-by-count":15,"title":["Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves"],"prefix":"10.1090","volume":"90","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philipp","family":"Reiter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2021,5,6]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1134\/S1061920814040013","article-title":"On the normal form of knots","volume":"21","author":"Avvakumov, S.","year":"2014","journal-title":"Russ. 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