Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation

Understand

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval.

• The discretization is based on the equation's gradient flow structure with respect to the Wasserstein distance.
• The scheme inherits various properties of the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/maximum principles.
• As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition.