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We study polygonal analogues of several moving boundary problems and theirtime discretization which preserves the constant area speed property. Weestablish various polygonal analogues of geometric formulas for movingboundaries and make use of the geometric formulas for our numerical scheme andits analysis of general constant area speed motion of polygons. Accuracy andefficiency of our numerical scheme are checked through numerical simulationsfor several polygonal motions such as motion by curvature and area-preservingadvected flow etc.

Second order numerical scheme for motion of polygonal curves with constant area speed