Hello everyone. My current research involves to deal with PDE which describe the migration of diffusion of a solute. In this case I would like to get the weak form of this PDE and after that apply FEM,

dXc/dt-d/dz[DXc/(RT)dMu/dz]=0

where Xc, is the solute content (Field variable), D diffusion coefficient (concentration dependent), Mu is the chemical potential(concentration dependent), and RT are the universal ga sconstant and temperature respectively. My doubt is how to do discretization of the term dMu/dz, since the fiel variable is Xc in my week form? Do I have to use shape function?

Thanks in advance. Post tada. there is pdf file where specify better my formulation. Thanks in advance.