  We introduce a novel formulation for the evolution of parametric curves by
anisotropic curve shortening flow in ${\mathbb R}^d$, $d\geq2$. The
reformulation hinges on a suitable manipulation of the parameterization's
tangential velocity, leading to a strictly parabolic differential equation.
Moreover, the derived equation is in divergence form, giving rise to a natural
variational numerical method. For a fully discrete finite element approximation
based on piecewise linear elements we prove optimal error estimates. Numerical
simulations confirm the theoretical results and demonstrate the practicality of
the method.
