论文标题
弹性流与切向网格运动的方案的收敛性
Convergence of a scheme for elastic flow with tangential mesh movement
论文作者
论文摘要
封闭曲线的弹性流可以涉及显着变形。基于网格的近似方案需要切向重新分布顶点，以进行长期计算。我们介绍并分析一种将Dirichlet Energy用于此目的的方法。该方法还有效地惩罚了曲线的长度，平衡形状等效于弹性能量的固定点随长度功能增强。我们的数值方法基于线性参数有限元。遵循K deckelnick和G dziuk（Math Comp 78，266（2009），645-671），我们证明并建立了误差估计，并指出与长度函数相比，添加Dirichlet Energy可以简化分析。我们还提出了一个简单的半平时离散化，并讨论了支持该理论的一些数值结果。
Elastic flow for closed curves can involve significant deformations. Mesh-based approximation schemes require tangentially redistributing vertices for long-time computations. We present and analyze a method that uses the Dirichlet energy for this purpose. The approach effectively also penalizes the length of the curve, and equilibrium shapes are equivalent to stationary points of the elastic energy augmented with the length functional. Our numerical method is based on linear parametric finite elements. Following the lines of K Deckelnick, and G Dziuk (Math Comp 78, 266 (2009), 645-671) we prove convergence and establish error estimates, noting that the addition of the Dirichlet energy simplifies the analysis in comparison with the length functional. We also present a simple semi-implicit time discretization and discuss some numerical result that support the theory.
