The Scharfetter--Gummel scheme for aggregation-diffusion equations

Autor:	Schlichting, André, Seis, Christian
Rok vydání:	2020
Předmět:	Mathematics - Numerical Analysis Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
DOI:	10.1093/imanum/drab039
Popis:	In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the quadratic, nonlocal flux term. This scheme is analyzed concerning well-posedness and convergence towards solutions to the continuous problem. Also, it is proven that the numerical scheme has several structure-preserving features. More specifically, it is shown that the discrete solutions satisfy a free-energy dissipation relation analogous to the continuous model. Consequently, the numerical solutions converge in the large time limit to stationary solutions, for which we provide a thermodynamic characterization. Numerical experiments complement the study. Comment: 37 pages. Accepted version with existence and stability argument without CFL-conditions. In addition, some numerical experiments are added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.13981 Zobrazit plný text záznamu View this record from Arxiv