On an elastic flow for parametrized curves in $\mathbb{R}^n$ suitable for numerical purposes

TL;DR

This paper studies a numerically suitable elastic flow for parametrized curves in multi-dimensional space, proving that the flow persists indefinitely over time, which is important for computational applications.

Contribution

It establishes the global existence of a modified elastic flow for closed curves in ^n, enhancing its applicability for numerical simulations.

Findings

Flow exists globally in time

Flow is a variant suitable for numerical purposes

Supports long-term numerical analysis

Abstract

In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in $\mathbb{R}^{n}$ was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating that the flow exists globally in time.