A hybrid mass transport finite element method for Keller-Segel type systems
This method provides a more efficient numerical approach for solving reaction-taxis-diffusion systems, which are important in biological pattern formation and chemotaxis modeling.
The paper introduces a hybrid mass transport finite element method for Keller-Segel type systems that handles concentrated and diffusive regions, travelling waves, and merging phenomena. The scheme outperforms dedicated mesh-adapted AMR schemes due to its built-in mass adaption.
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.