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

Daniel Matthes, Horst Osberger
2014 Mathematical Modelling and Numerical Analysis  
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. We
more » ... ype condition. We also present results from numerical experiments.
doi:10.1051/m2an/2013126 fatcat:wwvpf2c2cngtrg626qhmn6k2he