We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusionequation on an interval. The discretization is based on the equation’s gradient flowstructure with respect to the Wasserstein distance. The scheme inherits various propertiesfrom the continuous flow, like entropy monotonicity, mass preservation, metric contractionand minimum/ maximum principles. As the main result, we give a proof of convergence in thelimit of vanishing mesh size under a CFL-type condition. We also present results fromnumerical experiments.
