I would like to implement a Fokker-Planck equation in Fenics, but I don’t know how to formulate the variational form of the PDE. I’ve looked at various examples, but am too inexperienced with PDEs to adapt one to my needs. Generally solving PDEs is out of my area of expertise and after some time reading through the documentation I realize that I likely need to start at the very beginning to get this right. So any help would be greatly appreciated.
\frac{\partial p(v,t)}{\partial t} = -\frac{\partial}{\partial v} \mu(v,t)p(v,t) + \frac{\partial^2}{\partial v^2} D(v,t)p(v,t)
The advective coefficient and diffusion coefficent are stationary (\mu(v,t) = 1, D(v,t)=1), but I’d like to make \mu(v,t) time dependent when the stationary case works. The boundary conditions are a Dirac pulse at t=0 and absorbing bounds at \pm B:
p(v,t_0) = \delta(v)
p(\pm B,t) = 0
Again - any help in implementing this in fenics would be greatly appreciated.
I’m sorry for the inconvenience if this is not the right place to ask this question.