Much evidence shows that the early stages of skeletal pattern formation in the developing vertebrate limb rely on complex dynamics, in which Different growth factors, several types of cells and distinct zones are involved. It would be much of interest to get insight into this intriguing biological phenomenon. We are interested in using mathematical and computational techniques to simulate the skeletal pattern formation during chick limb bud development, in which the system could be described by some reaction-diffusion equations. The discontinuous Galerkin finite element method is applied to deal with the irregular and asymmetric geometry domains and operator splitting is used to overcome the challenges of stiffness of the system and the restriction of the time step size. Based on the parameter studies and different geometry domains, we have gotten both spots and strips patterns, which are consistent with the biological experiment. In the rectangular domains, we have gotten one strip, followed by two and three strips, which is similar to the progression observed during the natural development of a chick limb.
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