Journal of Scientific Computing

, Volume 24, Issue 2, pp 247–262

A Moving Grid Finite Element Method for the Simulation of Pattern Generation by Turing Models on Growing Domains

  • Anotida Madzvamuse
  • Philip K. Maini
  • Andrew J. Wathen
Article

Abstract

Numerical techniques for moving meshes are many and varied. In this paper we present a novel application of a moving grid finite element method applied to biological problems related to pattern formation where the mesh movement is prescribed through a specific definition to mimic the growth that is observed in nature. Through the use of a moving grid finite element technique, we present numerical computational results illustrating how period doubling behaviour occurs as the domain doubles in size.

Keywords

Moving meshes moving grid finite elements reaction–diffusion systems Turing instability 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Anotida Madzvamuse
    • 1
  • Philip K. Maini
    • 2
  • Andrew J. Wathen
    • 3
  1. 1.Mathematics DepartmentAuburn UniversityAuburnUSA
  2. 2.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK
  3. 3.Oxford University Computing LaboratoryOxfordUK

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