Title of article :
Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion
Author/Authors :
Lin، نويسنده , , Zhigui and Ruiz-Baier، نويسنده , , Ricardo and Tian، نويسنده , , Canrong، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2014
Abstract :
This paper is concerned with the study of pattern formation for an inhomogeneous Brusselator model with cross-diffusion, modeling an autocatalytic chemical reaction taking place in a three-dimensional domain. For the spatial discretization of the problem we develop a novel finite volume element (FVE) method associated to a piecewise linear finite element approximation of the cross-diffusion system. We study the main properties of the unique equilibrium of the related dynamical system. A rigorous linear stability analysis around the spatially homogeneous steady state is provided and we address in detail the formation of Turing patterns driven by the cross-diffusion effect. In addition we focus on the spatial accuracy of the FVE method, and a series of numerical simulations confirm the expected behavior of the solutions. In particular we show that, depending on the spatial dimension, the magnitude of the cross-diffusion influences the selection of spatial patterns.
Keywords :
Brusselator model , Cross-diffusion effect , spatial patterns , Finite volume element method
Journal title :
Journal of Computational Physics
Journal title :
Journal of Computational Physics