论文标题
凸面性和外围降低参数有限元法，用于区域保护曲线缩短流量
A convexity-preserving and perimeter-decreasing parametric finite element method for the area-preserving curve shortening flow
论文作者
论文摘要
我们提出和分析了一个半差异参数有限元方案，用于解决区域保护曲线缩短流。该方案基于Dziuk的方法（Siam J.Numer。Anal。36（6）：1808-1830，1999），用于各向异性曲线缩短流。我们证明该方案以最初的凸曲线保留了流量的两个基本几何结构：（i）凸出属性属性，以及（ii）周边降低的属性。据我们所知，数值方案的具有凸度的属性是第一次严格证明流量的数值方案。此外，还建立了半分化方案的误差估计值，并提供了数值结果以证明结构具有实现的属性以及该方案的准确性。
We propose and analyze a semi-discrete parametric finite element scheme for solving the area-preserving curve shortening flow. The scheme is based on Dziuk's approach (SIAM J. Numer. Anal. 36(6): 1808-1830, 1999) for the anisotropic curve shortening flow. We prove that the scheme preserves two fundamental geometric structures of the flow with an initially convex curve: (i) the convexity-preserving property, and (ii) the perimeter-decreasing property. To the best of our knowledge, the convexity-preserving property of numerical schemes which approximate the flow is rigorously proved for the first time. Furthermore, the error estimate of the semi-discrete scheme is established, and numerical results are provided to demonstrate the structure-preserving properties as well as the accuracy of the scheme.
