We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discrete curve-shortening polygonal evolution law. The proposed evolution law is fully implicit, and the key to the derivation is to devise the definitions of tangent and normal vectors and tangential and normal velocities at each vertex in an implicit manner. Numerical experiments show that the proposed method allows the use of relatively large time step sizes and also captures the area-preserving or dissipative property in good accuracy.

中文翻译：

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移动边界问题的全离散曲线缩短多边形发展规律

我们考虑具有曲线缩短特性的运动边界问题的数值积分，例如平均曲率流和Hele-Shaw流。我们提出了一个完全离散的曲线缩短多边形发展规律。拟议的演化定律是完全隐式的，推导的关键是隐式设计每个顶点的切线和法向矢量以及切线和法向速度的定义。数值实验表明，该方法可以使用较大的时间步长，并且可以很好地捕获面积保留或耗散特性。