Numerical solution of constrained curvature flow for closed planar curves

Abstract

This paper presents results of computational studies of the evolution law for the constrained mean curvature flow. The considered motion law originates in the theory of phase transitions in crystalline materials. It describes the evolution of closed embedded curves with constant enclosed area. In the paper, the motion law is treated by the parametric method, which leads into the system of degenerate parabolic equations for the parametric description of the curve. This system is numerically solved by means of the flowing finite volume method enhanced by tangential redistribution. Qualitative and quantitative results of computational studies are presented.