发表机构
Otto-von-Guericke-Universität Magdeburg; Università di Trento（奥托·冯·格里克马格德堡大学; 特伦托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种二阶精度的过滤时间步进有限元格式，用于任意余维数中开闭曲线的曲率缩短流，证明了最优误差界，数值实验验证了其准确性和实用性。
AI 中文摘要
我们针对任意余维数中开曲线和闭曲线的曲率缩短流，提出了一种在时间上具有二阶精度的过滤时间步进有限元格式。开曲线被假定在给定区域 $\Omega \subset \mathbb R^n$（$n\geq2$）内演化，并与外部边界 $\partial\Omega$ 正交相交。我们证明了 $L^2$ 范数和 $H^1$ 范数的最优误差界。在实际计算中，每个时间步只需求解一个线性系统。数值实验证实了所引入方法的准确性和实用性，包括渐近等分布性质。
英文摘要
We propose a filtered time stepping finite element scheme for curve shortening flow of open and closed curves in arbitrary codimension that is second-order accurate in time. Open curves are assumed to evolve inside a given domain $Ω\subset \mathbb R^n$, $n\geq2$, and meet the external boundary $\partialΩ$ orthogonally. We prove optimal error bounds for the $L^2$-- and $H^1$--norms. In practice only a single linear system needs to be solved at each time step. Numerical experiments confirm the accuracy and practicality of the introduced method, including an asymptotic equidistribution property.
Comments26 pages, 6 figures
