English

Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions

Analysis of PDEs 2019-12-16 v1

Abstract

We present a new finite volume method for computing numerical approximations of a system of nonlocal transport equation modeling interacting species. This method is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet, Convergence analysis of upwind type schemes for the aggregation equation with pointy potential, Ann. Henri. Lebesgue 2019], where the nonlocal continuity equations are 10 treated as conservative transport equations with a nonlocal, nonlinear, rough velocity field. We analyze some properties of the method, and illustrate the results with numerical simulations.

Keywords

Cite

@article{arxiv.1912.06423,
  title  = {Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions},
  author = {Anissa Keurti and Thomas Rey},
  journal= {arXiv preprint arXiv:1912.06423},
  year   = {2019}
}

Comments

8 pages, 2 figures

R2 v1 2026-06-23T12:45:01.350Z