Numerical simulation for clustering and pattern formation in active colloids with mass-preserving characteristic finite element method

Abstract

We consider the numerical approximations to simulate the active colloids dynamic process. One linear, decoupled, mass-preserving scheme is proposed, in which mass-preserving characteristic finite element method is utilized for the density equation of active colloids, and the traditional Galerkin finite element methods is used for the polarization dynamics equation and self-secreted chemical density equation. This method not only improves the computational efficiency but also keeps the mass conservation. We analyze the convergence of this method and give the corresponding error estimate under some regularity assumptions of the solution. Numerical experiments are carried out to support the theoretical analysis. The proposed method is also applied to simulate the active colloids dynamic process for the clustering and pattern formation in chemoattraction and chemorepulsion, respectively.