Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
Numerical Analysis
2016-11-23 v2
Abstract
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient flow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this properties with various examples in spatial dimension one and two.
Keywords
Cite
@article{arxiv.1605.05921,
title = {Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms},
author = {José A. Carrillo and Helene Ranetbauer and Marie-Therese Wolfram},
journal= {arXiv preprint arXiv:1605.05921},
year = {2016}
}