Research
Monday, 15 September 2014 23:45

## A discontinuous Galerkin method on kinetic flocking models

Changhui Tan

Mathematical Models and Methods in Applied Sciences, Volume 27, No 7, pp. 1199-1221 (2017).

Abstract

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker–Smale [Emergent behaviors in flocks, IEEE Trans. Autom. Control. 52 (2007) 852–862] and Motsch–Tadmor [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 144 (2011) 923– 947] models. We first establish a well-posedness theory and large-time flocking behavior for the kinetic systems, which indicates a concentration in velocity variable in infinite time. We then apply a discontinuous Galerkin method to treat the asymptotic $$\delta$$-singularity, and construct high-order positive-preserving schemes to solve kinetic flocking systems.