A finite element approach to capture Turing patterns of autocatalytic Brusselator model

摘要

In this article, the authors approximate solution to the Brusselator model by Galerkin finite element method and present a priori error estimate for the approximation. Further, we study the stability of the model when cross-diffusion is present. We find that the cross-diffusion increases the wave number of the solution. Using Crank-Nicolson method with Predictor-Corrector scheme for discretization of time, we propose an algorithm for numerical simulation of the solution. Lastly, some numerical examples are considered to illustrate the efficiency and accuracy of the method and to plot the Turing patterns of the model.