High Order Positive schemes for the Keller-Segel Problem

PI (U. Sevilla): Francisco Guillén González 

PI (U. Nantes): Mazen Saad

Abstract: This project concerns the mathematical analysis and the construction of accurate numerical schemes for nonlinear parabolic systems arising from the modelling of chemotaxis phenomena. Our goal is to elaborate and analyze numerically the most common system in chemotaxis namely the Keller–Segel system. Our interest is the degenerate Keller–Segel modelling the volume filling effect and the standard nondegenerate Keller-Segel system with linear or subquadratic production term respect to the cell density. We focus on the construction of monotone combining finite volume conforming finite element scheme on triangular mesh and on positive Discrete Duality Finite Volume on general nonconforming mesh.