具有恒定面积速度的多边形曲线运动的二阶数值格式
Second order numerical scheme for motion of polygonal curves with constant area speed
AI总结：
针对具有恒定面积速度的多边形曲线运动，提出并分析了一种基于几何公式的二阶数值格式，通过曲率运动和面积保持对流等模拟验证了其精度和效率。
摘要：
我们研究了几个移动边界问题的多边形类比及其时间离散化，该离散化保持了恒定面积速度性质。我们建立了移动边界的各种多边形几何公式，并将这些几何公式用于我们的数值格式及其对多边形恒定面积速度运动的一般分析。通过曲率运动和面积保持对流等几种多边形运动的数值模拟，检验了我们数值格式的精度和效率。
英文摘要：
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of general constant area speed motion of polygons. Accuracy and efficiency of our numerical scheme are checked through numerical simulations for several polygonal motions such as motion by curvature and area-preserving advected flow etc.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
