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A moving grid finite element method applied to a model biological pattern generator |
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| Authors: | Anotida Madzvamuse Andrew J. Wathen Philip K. Maini |
| Affiliation: | a Mathematics Department, 221 Parker Hall, Auburn University, AL 36849-3510, USA;b Numerical Analysis Group, Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK;c Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24–29 St. Giles’, Oxford OX1 3LB, UK |
| Abstract: | Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis. |
| Keywords: | Moving grid finite elements Reaction– diffusion systems Turing instability Colour pattern formation Butterfly wing Papilio dardanus |
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