Barrett, John W. and Garcke, Harald and Nürnberg, Robert
Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves.
Preprintreihe der Fakultät Mathematik 1/2011,
Deckelnick and Dziuk (2009) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of Willmore flow/elastic flow of closed curves in Rd, d ≥ 2. We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in Barrett, Garcke, and Nürnberg (2007b, 2008b, 2010b), in particular an equidistribution mesh property. For this new approximation, we obtain also a stability bound for a continuous-in-time semidiscrete scheme. Apart from
the isotropic situation, we also consider the case of an anisotropic elastic energy. In addition to the evolution of closed curves, we also consider the isotropic and anisotropic
elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions.
|Item Type:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||elastic flow, Willmore flow, Navier boundary conditions, clamped boundary conditions, parametric finite elements, tangential movement, anisotropy|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||13 Apr 2011 04:08|
|Last Modified:||21 Jul 2011 02:11|