  Based on a recent novel formulation of parametric anisotropic curve
shortening flow, we analyse a fully discrete numerical method of this geometric
evolution equation. The method uses piecewise linear finite elements in space
and a backward Euler approximation in time. We establish existence and
uniqueness of a discrete solution, as well as an unconditional stability
property. Some numerical computations confirm the theoretical results and
demonstrate the practicality of our method.
