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A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. Themethod is based on the flowing finite volume discretization of the intrinsicpartial differential equation for updating the position vector of evolvingfamily of plane curves. A curve can be evolved in the normal direction by acombination of fourth order terms related to the intrinsic Laplacian of thecurvature, second order terms related to the curvature, first order termsrelated to anisotropy and by a given external velocity field. The evolution isnumerically stabilized by an asymptotically uniform tangential redistributionof grid points yielding the first order intrinsic advective terms in thegoverning system of equations. By using a semi-implicit in time discretizationit can be numerically approximated by a solution to linear penta-diagonalsystems of equations (in presence of the fourth order terms) or tri-diagonalsystems (in the case of the second order terms). Various numerical experimentsof plane curve evolutions, including, in particular, nonlinear, anisotropic andregularized backward curvature flows, surface diffusion and Willmore flows, arepresented and discussed.

A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations