Mathematics

We consider the motion of parametric curves by anisotropiccurve shortening flow. We propose a strictly parabolic system of PDEs forthe position vector whose solution satisfies the corresponding evolution law.This system is discretized by linear finite elements and optimal H^1 errorbounds are proved in the semidiscrete case. In addition, we consider some fully discrete schemes and prove their unconditional stability. Finally, we present several numerical experiments that demonstrate the robustness and practicality of the introduced schemes.This is joint work with Klaus Deckelnick.