A moving grid finite element method applied to a model biological pattern generator

Author: Adams, Andrew J. Wathen, Anotida Madzvamuse, Aragón, Aragón, Baines, Baines, Balkarei, Barrio, Barrio, Batima, Blom, Brenner, Carlson, Carlson, Crampin, Edelstein-Keshet, Gierer, Gray, Gray, Jimack, Johnson, Kondo, Krinsky, Madzvamuse, Madzvamuse, Maini, Meinhardt, Miller, Miller, Murray, Murray, Mçller, Nijhout, Nozakura, Painter, Philip K. Maini, Reddy, Saad, Schnakenberg, Segel, Sekimura, Sekimura, Sekimura, Sun, Thomas, Thomas, Turing, White
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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

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