37 citations · 91 across the 23 of their papers we have counts for
4 papers · 1 filter
Convergence of a finite volume scheme for a model for ants
Maria Bruna, Markus Schmidtchen, Oscar de Wit
We develop and analyse a finite volume scheme for a nonlocal active matter system known to exhibit a rich array of complex behaviours. The model under investigation was derived fro…
A Convergent Finite Volume Method for a Kinetic Model for Interacting Species
Julia I. M. Hauser, Valeria Iorio, Markus Schmidtchen
We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction system…
Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations
Rafael Bailo, Jose A. Carrillo, Hideki Murakawa +1
We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo,…
Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion
José A. Carrillo, Francis Filbet, Markus Schmidtchen
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cros…