Transport Models for Collective Dynamics in Biological Systems

Particles' method for porous medium equation

Pierre-Emmanuel Jabin

University of Maryland

We study the approximation of the porous medium equation by deterministic particles' methods. From a physical point of view, this corresponds to the classical idea that the porous medium model corresponds to some kind of pressure (i.e. repulsion) between particles. From a numerical point of view, particles' methods are both efficient and easy to implement. We will present explicit rates of convergence for those methods.