Article

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 MadzvamuseAffiliated withMathematics Department, Auburn University Email author 
  • , Philip K. MainiAffiliated withCentre for Mathematical Biology, Mathematical Institute, University of Oxford
  • , Andrew J. WathenAffiliated withOxford University Computing Laboratory

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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