Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2012) ELASTIC FLOW WITH JUNCTIONS: VARIATIONAL APPROXIMATION AND APPLICATIONS TO NONLINEAR SPLINES. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 22 (11): 1250037. ISSN 0218-2025, 1793-6314
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We consider stable semidiscrete approximations of parametrized curve networks for gradient flows of elastic type functionals. Here meaningful and relevant conditions at junction points, such as double and triple junctions, need to be derived and suitably discretized. Examples for double junction types are C-0 attachment and C-1 continuity. We develop strong and weak formulations for the elastic flow for curve networks with such junction points. For junctions with three or more curves, the conditions at the junctions are derived here for the first time. Possible applications include a simplified one-dimensional model of geometric biomembranes, as well as nonlinear splines in two and higher dimensions. The numerical results presented in this paper demonstrate the practicality of the introduced finite element approximations.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; PARAMETRIC APPROXIMATION; CURVES; COMPUTATION; Elastic flow; Willmore flow; parametric finite elements; tangential movement; curve networks; junctions; nonlinear splines |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2020 06:59 |
| Last Modified: | 06 May 2020 06:59 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17918 |
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