Numerical analysis of growth-mediated autochemotactic pattern formation in self-propelling bacteria

TL;DR

This paper presents a numerical method for simulating pattern formation in self-propelling bacteria influenced by growth and chemotaxis, revealing new wave patterns through computational experiments.

Contribution

It introduces a decoupled Galerkin finite element approach for modeling bacterial chemotactic patterns, with proven convergence and error estimates, and uncovers novel wave patterns.

Findings

New wave type patterns discovered in simulations

Method demonstrates convergence and accuracy

Supports theoretical analysis with numerical experiments

Abstract

In this paper, a decoupled characteristic Galerkin finite element procedure is provided for simulating growth-mediated autochemotactic pattern formation in self-propelling bacteria. In this procedure, a modified characteristic Galerkin method is established to solve the bacterial density equation, while the classical finite element procedure is considered for the self-secreted chemical density and polarization dynamics equations system. The convergence of this proposed method is considered under some regularity assumptions and the corresponding error estimate is derived. Numerical experiments are carried out to support the theoretical analysis. Furthermore, several new wave type pattern formations are found.