@Article{CMR-39-2,
author = {Miyazaki, Eiji and Tomoya, Kemmochi and Tomohiro, Sogabe and Zhang, Shao-Liang},
title = {A Structure-Preserving Numerical Method for the Fourth-Order Geometric Evolution Equations for Planar Curves},
journal = {Communications in Mathematical Research },
year = {2023},
volume = {39},
number = {2},
pages = {296--330},
abstract = {<p style="text-align: justify;">For fourth-order geometric evolution equations for planar curves
with the dissipation of the bending energy, including the Willmore and the
Helfrich flows, we consider a numerical approach. In this study, we construct
a structure-preserving method based on a discrete variational derivative method. Furthermore, to prevent the vertex concentration that may lead to numerical instability, we discretely introduce Deckelnick’s tangential velocity. Here,
a modification term is introduced in the process of adding tangential velocity.
This modified term enables the method to reproduce the equations’ properties
while preventing vertex concentration. Numerical experiments demonstrate
that the proposed approach captures the equations’ properties with high accuracy and avoids the concentration of vertices.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2022-0040},
url = {https://global-sci.com/article/81461/a-structure-preserving-numerical-method-for-the-fourth-order-geometric-evolution-equations-for-planar-curves}
}