Numerical Solution of linear drift-diffusion and pure drift equations on one-dimensional graphs
Numerical Analysis
2024-11-01 v2 Numerical Analysis
Abstract
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite Volume schemes with upwind flux to domains presenting bifurcation nodes with an arbitrary number of incoming and outgoing edges, and implicit time discretization. We show that the discrete problems admit positive unique solutions, and we test the methods on the intricate geometry of an electrical treeing.
Cite
@article{arxiv.2410.20931,
title = {Numerical Solution of linear drift-diffusion and pure drift equations on one-dimensional graphs},
author = {Beatrice Crippa and Anna Scotti and Andrea Villa},
journal= {arXiv preprint arXiv:2410.20931},
year = {2024}
}