Convergent lagrangian discretization for drift-diffusion with nonlocal aggregation

Abstract

A Lagrangian discretization for nonlinear aggregation-diffusion equations in one space dimension is presented, and its convergence is rigorously analyzed. In comparison to related works by the first author and Osberger (ESAIM Math Model Numer Anal 48:697–726, 2014; Found Comput Math 1–54, 2015) on Lagrangian schemes for drift-diffusion equations, convergence is proven directly on the level on the Lagrangian maps, without passage through the density formulation.