Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion

JOURNAL OF COMPUTATIONAL PHYSICS

卷:256

Article

Lin, Zhigui¹  Ruiz-Baier, Ricardo²  Tian, Canrong³ 

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China

[2] Ecole Polytech Fed Lausanne, MATHICSE SB, CH-1015 Lausanne, Switzerland

[3] Yancheng Inst Technol, Dept Basic Sci, Yancheng 224003, Peoples R China

关键词: Finite volume element method;    Brusselator model;    Cross-diffusion effect;    Spatial patterns;   

DOI  :  10.1016/j.jcp.2013.09.009

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free