Discrete anisotropic curve shortening flow

Anisotropic curve shortening flow is a geometric evolution of a curve and is equivalent to the gradient flow of anisotropic interface energy. We develop a numerical scheme for this nonlinear and degenerate problem, which is based on the fact that the evolution problem can be written formally as a linear partial differential equation on the interface itself. The scheme requires the solution of a tridiagonal complex linear system in each time step. We prove optimal error estimates in adequate norms for the semidiscrete scheme and provide numerical test computations. The scheme can also be applied to crystalline energies.