A finite element method for Turing pattern formation

Abstract: 

The aim of the thesis is to perform numerical simulations of Turing patterns for irregularly shaped domains.  In this setting, finite elements are an appropriate tool for the spatial discretisation. I outline Turing's theory of pattern formation, and describe how basic numerical techniques for parabolic problems are extended to treat coupled, semilinear reaction-diffusion equations of the type arising in this application.  The Gmsh program is used to perform the necessary mesh generation, and the numerical simulations are carried out with the help of FinElt.jl, a Julia package for finite element calculations.