A deterministic particle method for the porous media equation
Analysis of PDEs
2025-02-03 v1 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
This paper deals with the deterministic particle method for the equation of porous media (with p = 2). We establish a convergence rate in the Wasserstein-2 distance between the approximate solution of the associated nonlinear transport equation and the solution of the original one. This seems to be the first quantitative rate for diffusion-velocity particle methods solving diffusive equations and is achieved using a novel commutator estimate for the Wasserstein transport map.
Cite
@article{arxiv.2501.18745,
title = {A deterministic particle method for the porous media equation},
author = {Amina Amassad and Datong Zhou},
journal= {arXiv preprint arXiv:2501.18745},
year = {2025}
}