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 to analyse 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.
Cite this article
Michal Beneš, Shigetoshi Yazaki, Masato Kimura, Second order numerical scheme for motion of polygonal curves with constant area speed. Interfaces Free Bound. 11 (2009), no. 4, pp. 515–536DOI 10.4171/IFB/221