Mainak Mandal: Structure preserving finite volume schemes for aggregation-diffusion equations

Vortragender/Speaker: Mainak Mandal (IWR)
Ansprechpartner/Contact: Dr. Simon Praetorius
Video conference (BBB): https://tud.link/phf1

Titel/Title:
Structure preserving finite volume schemes for aggregation-diffusion equations

Zusammenfassung/Abstract:
Non-local aggregation-diffusion equations can be used to describe large groups of particles at the macro scale. In particular, these equations can be used to model a biological system of interacting species involving dispersal, drift, and non-local interactions. The existence and uniqueness of solutions to these equations are well known in literature. We present the construction and convergence of a semi-discrete finite volume scheme, that preserves the structural properties of the equations such as energy dissipation and non-negativity on general meshes. The key to obtaining convergence is a discrete gradient estimate of the dispersal term, then using this in a modified Aubin-Lions lemma to obtain compactness of the density leading to convergence.