A hybrid mass transport finite element method for Keller-Segel type systems

TL;DR

This paper introduces a novel splitting finite element method for Keller-Segel type systems that effectively handles concentrated and diffusive regions, traveling waves, and merging phenomena using a mass transport approach.

Contribution

It presents a new splitting scheme combining mass transport with finite element methods, enabling efficient simulation of complex reaction-taxis-diffusion systems.

Findings

Effective handling of concentrated and diffusive regions.

Accurate simulation of traveling waves and merging phenomena.

Superior performance compared to mesh-adapted schemes.

Abstract

We propose a new splitting scheme for general reaction-taxis-diffusion systems in one spatial dimension capable to deal with simultaneous concentrated and diffusive regions as well as travelling waves and merging phenomena. The splitting scheme is based on a mass transport strategy for the cell density coupled with classical finite element approximations for the rest of the system. The built-in mass adaption of the scheme allows for an excellent performance even with respect to dedicated mesh-adapted AMR schemes in original variables.