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

Authors:
Anotida Madzvamuse;Philip K. Maini;Andrew J. Wathen
Affiliations:
Mathematics Department, Auburn University, Auburn, USA 36849;Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK OX1 3LB;Oxford University Computing Laboratory, Oxford, UK OX 13QD
Venue:
Journal of Scientific Computing
Year:
2005

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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.