论文标题
边界值问题的数值近似值曲率流和弹性流的弹性流量
Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds
论文作者
论文摘要
我们介绍了曲率流（曲线缩短流）和弹性流（曲线拉直流）的边界值问题的变异近似值，这些流量（曲线拉直流动流）在二维riemannian歧管中，这些歧管形式平坦。对于不断发展的开放曲线，我们提出尊重适当梯度流结构的自然边界条件。基于合适的弱制剂，我们使用分段线性元素引入有限元近似值。对于某些方案，可以显示稳定性结果。衍生方案可以在非常不同的情况下采用。例如，我们将方案应用于绿色指标，以便计算平均曲率流量的旋转自身对称的自我缩合器。此外，我们利用这些方案来计算与多组分相位字段模型中最佳接口配置文件相关的测量学。
We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open curves we propose natural boundary conditions that respect the appropriate gradient flow structure. Based on suitable weak formulations we introduce finite element approximations using piecewise linear elements. For some of the schemes a stability result can be shown. The derived schemes can be employed in very different contexts. For example, we apply the schemes to the Angenent metric in order to numerically compute rotationally symmetric self-shrinkers for the mean curvature flow. Furthermore, we utilise the schemes to compute geodesics that are relevant for optimal interface profiles in multi-component phase field models.
