Open Access
Volume 57, Number 2, March-April 2023
Page(s) 445 - 466
Published online 23 March 2023
  1. N. Balzani and M. Rumpf, A nested variational time discretization for parametric Willmore flow. Interfaces Free Bound. 14 (2012) 431–454. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.W. Barrett, H. Garcke and R. Nürnberg, A parametric finite element method for fourth order geometric evolution equations. J. Comput. Phys. 222 (2007) 441–467. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.W. Barrett, H. Garcke and R. Nürnberg, Numerical approximation of gradient flows for closed curves in ℝd. IMA J. Numer. Anal. 30 (2010) 4–60. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.W. Barrett, H. Garcke and R. Nürnberg, Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Numer. Math. 120 (2012) 489–542. [Google Scholar]
  5. S. Bartels, A simple scheme for the approximation of the elastic flow of inextensible curves. IMA J. Numer. Anal. 33 (2013) 1115–1125. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bondarava, Stability and error analysis for a numerical scheme to approximate elastic flow. Ph.D. thesis, Otto-von-Guericke-Universität Magdeburg (2015). [Google Scholar]
  7. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, in Texts in Applied Mathematics, 3rd edition. Vol. 15. Springer (2008). [Google Scholar]
  8. K. Deckelnick and G. Dziuk, On the approximation of the curve shortening flow, in Calculus of Variations, Applications and Computations (Pont-à-Mousson, 1994). Vol. 326 of Pitman Res. Notes Math. Ser. Longman Sci. Tech., Harlow (1994) 100–108. [Google Scholar]
  9. K. Deckelnick and G. Dziuk, Error analysis for the elastic flow of parametrized curves. Math. Comp. 78 (2009) 645–671. [Google Scholar]
  10. U. Dierkes, S. Hildebrandt and F. Sauvigny, Minimal surfaces, in Vol. 339 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edition. Springer, Heidelberg (2010). With assistance and contributions by A. Küster and R. Jakob. [Google Scholar]
  11. G. Dziuk, E. Kuwert and R. Schätzle, Evolution of elastic curves in ℝn: existence and computation. SIAM J. Math. Anal. 33 (2002) 1228–1245 (electronic). [Google Scholar]
  12. C.M. Elliott and H. Fritz, On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick. IMA J. Numer. Anal. 37 (2017) 543–603. [MathSciNet] [Google Scholar]
  13. C.M. Elliott, B. Stinner and C. Venkataraman, Modelling cell motility and chemotaxis with evolving surface finite elements. J. R. Soc. Interface 9 (2012) 3027–3044. [Google Scholar]
  14. J. Hu and B. Li, Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow. Numer. Math. 152 (2022) 127–181. [Google Scholar]
  15. N. Koiso, On the motion of a curve towards elastica, in Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992). Vol. 1 of Sémin. Congr. Soc. Math. France, Paris (1996) 403–436. [Google Scholar]
  16. B. Kovács, B. Li and C. Lubich, A convergent evolving finite element algorithm for Willmore flow of closed surfaces. Numer. Math. 149 (2021) 595–643. [Google Scholar]
  17. J. Langer and D.A. Singer, Curve straightening and a minimax argument for closed elastic curves. Topology 24 (1985) 75–88. [Google Scholar]
  18. C.-C. Lin and H.R. Schwetlick, On a flow to untangle elastic knots. Calc. Var. Part. Differ. Equ. 39 (2010) 621–647. [CrossRef] [Google Scholar]
  19. J.A. Mackenzie, M. Nolan, C.F. Rowlatt and R.H. Insall, An adaptive moving mesh method for forced curve shortening flow. SIAM J. Sci. Comput. 41 (2019) A1170–A1200. [Google Scholar]
  20. C. Mantegazza, A. Pluda and M. Pozzetta, A survey of the elastic flow of curves and networks. Milan J. Math. 89 (2021) 59–121. [Google Scholar]
  21. The Mathworks Inc., MATLAB version (R2022a). Natick, Massachusetts (2022). [Google Scholar]
  22. A. Polden, Curves and surfaces of least total curvature and fourth-order flows. Ph.D. thesis, Universität Tübingen (1996). [Google Scholar]
  23. P. Pozzi, Computational anisotropic Willmore flow. Interfaces Free Bound. 17 (2015) 189–232. [CrossRef] [MathSciNet] [Google Scholar]
  24. P. Pozzi, On an elastic flow for parametrized curves in ℝn suitable for numerical purposes. Preprint arXiv:2205.04178 (2022). [Google Scholar]
  25. P. Pozzi and B. Stinner, On motion by curvature of a network with a triple junction. SMAI J. Comput. Math. 7 (2021) 27–55. [Google Scholar]
  26. C. Truesdell, The influence of elasticity on analysis: the classic heritage. Bull. Amer. Math. Soc. (N.S.) 9 (1983) 293–310. [CrossRef] [MathSciNet] [Google Scholar]
  27. Y. Wen, L2 flow of curve straightening in the plane. Duke Math. J. 70 (1993) 683–698. [MathSciNet] [Google Scholar]
  28. Y. Wen, Curve straightening flow deforms closed plane curves with nonzero rotation number to circles. J. Differ. Equ. 120 (1995) 89–107. [CrossRef] [Google Scholar]

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