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

Zhigui Lin, Ricardo Ruiz-Baier, Canrong Tian

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19 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)806-823
Number of pages18
JournalJournal of Computational Physics
Publication statusPublished - 1 Jan 2014
Externally publishedYes


  • Brusselator model
  • Cross-diffusion effect
  • Finite volume element method
  • Spatial patterns

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