| Autor: |
Hraivoronska, Anastasiia, Schlichting, André, Tse, Oliver |
| Rok vydání: |
2023 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
In this paper, we explore the convergence of the semi-discrete Scharfetter-Gummel scheme for the aggregation-diffusion equation using a variational approach. Our investigation involves obtaining a novel gradient structure for the finite volume space discretization that works consistently for any non-negative diffusion constant. This allows us to study the discrete-to-continuum and zero-diffusion limits simultaneously. The zero-diffusion limit for the Scharfetter-Gummel scheme corresponds to the upwind finite volume scheme for the aggregation equation. In both cases, we establish a convergence result in terms of gradient structures, recovering the Otto gradient flow structure for the aggregation-diffusion equation based on the 2-Wasserstein distance. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
