Can You Help With Finite Element Analysis in Cylindrical Coordinates?

[colinven]

I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with coordinates (r,z).

I know how to do FEM in 2D using cartesian coordinates. Do any of you know how to do FEM in 3D using cylindrical coordinates; with a domain that is essentially 2D?

 

[Geofleur]

I am not sure if this would work, but here is the idea: Consider a vertical cross-section of the cone. It will look like a triangle. The solution on the left side of the triangle will be the same as on the right, so consider just the right side. This triangle has coordinates that look just like Cartesian x,y coordinates, except with x replaced by r and y replaced by z. Your differential equation will not have any $\phi$ dependence. So treat it just like the Cartesian 2D case that you already know how to solve. Set up a triangular FE grid, use the 2D hat functions, etc.

 

[a_potato]

You need to transform your equations from 2d Cartesian to 2d cylindrical, taking care on all the differential operators (not sure what equations you're using). You can then discretise these using conventional finite element techniques (e.g galerkin or similar). Note: Cartesian xy will yield different solutions to rz