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

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

2008-05-29

arxiv.org/abs/0805.4469v1

Mathematics

Numerical Analysis

25 pages, 8 figures, 2 tables, 17 references

Scientific paper

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.

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