A monotone finite volume scheme for linear drift-diffusion and pure drift equations on one-dimensional graphs
Year: 2025
Type: article
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 electrical treeing.
Source: Networks and Heterogeneous Media
DOI: 10.3934/nhm.2025029
Authors: Beatrice Crippa, Anna Scotti, Andrea Villa, Ricerca Sul Sistema Energetico (RSE), Milano 20134, Italy
Institutions: Politecnico di Milano, Ricerca sul Sistema Energetico (Italy)
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411288796