  In this paper, we develop an energy dissipative numerical scheme for gradient
flows of planar curves, such as the curvature flow and the elastic flow. Our
study presents a general framework for solving such equations. To discretize
time, we use a similar approach to the discrete partial derivative method,
which is a structure-preserving method for the gradient flows of graphs. For
the approximation of curves, we use B-spline curves. Owing to the smoothness of
B-spline functions, we can directly address higher order derivatives. In the
last part of the paper, we consider some numerical examples of the elastic
flow, which exhibit topology-changing solutions and more complicated evolution.
Videos illustrating our method are available on YouTube.
