Young Researchers Workshop: Ki-Net 2012-2019

A second-order numerical method for the aggregation equations

Susanne Solem

Norwegian University of Science and Technology

Inspired by TVD limiter-based second-order schemes for conservation laws, we derive a formally second-order accurate numerical method for measure valued multi-dimensional aggregation equations. These equations are ubiquitous in modelling concentration in applied mathematics, and find many applications in biological sciences (to name a few: swarming, bacterial chemotaxis, and opinion dynamics). The proposed method is motivated by a neat equivalence between a specific one-dimensional aggregation equation and a Burgers-type equation (proved by Bonaschi, Carrillo, Di Francesco, and Peletier in 2015). Furthermore, the resulting numerical scheme is validated by a proof of convergence in the 1-Wasserstein metric and a selection of numerical experiments.