A boundary-finite element method for diffusion over a curved surface.

The well known diffusion equation is used to simulate the spread of a quantity over a flat surface (in 2D) or through space (in 3D). However, the standard diffusion equation cannot be used to model the spread of a quantity over a curved surface such as the surface of an of an object in 3D space. However, if the surface is approximated by a set of flat, triangular elements then the diffusion equation can be applied to each element in terms of local variables and then mapped into the global variables using a relatively simple change of variables. This leads to a diffusion type equation with a different diffusion tensor in each element. This equation can then be solved using a boundary-finite element method. <br/><br/>The method is then used to simulate the changes in the density of biological cells on a surface as they migrate due to changes in the concentration of a growth factor. <br/>