Poisson's problem in polar coordinates

Hello FEniCS community,

I know that FEniCS works by default with Cartesian coordinates. I would like to solve Poisson’s problem in cylindrical coordinates so that I could extrapolate the idea to more complex systems in coordinates other than Cartesian.

The PDE is as follows:

- \frac{1}{r}\frac{\partial}{\partial r}\left(r{\partial u(r,\phi)\over\partial r}\right)- \frac{1}{r^2} {\partial^2 u(r,\phi)\over\partial \phi^2} = f(r,\phi)

Could you give me a hint on its variational form and how to incorporate and solve it in FEniCS?

Best regards,

I am also new to the community, and here is a related post I had written about obtaining the variational formulation in Cartesian coordinates, given its polar equivalent. Hopefully it helps.