12:14 PM
The problems with a FEM approach in your case are :
1) FEM are used to solve boundary conditions problems.That is to say : you are looking for a function in a domain and you know the value of the function (or its derivative, or a mix, or something like that) at the boundaries.
In your case the problem is obfuscated by the fact that if there were a value at the boundary y==0, x1<x<x2, it would be infinite, because of the null thickness of the disk. This secondary problem is not correlated.
So let's suppose that the disk has a certain non-null thickness. The problem is that you don't know what are the values of the function at this boundary. It is not closely related to the boundary of the matter (in your case, but not in electrostatics because we have conductor material = equipotial = Dirichlet Boundary condition)
2) I think that FEM would probably deal with a null thickness disk (with whatever kind of boundary condition Dirichlet, Neumann, that is to say not what you need), but I do not garanty this. It seems that some people trends to think that it is a problem.
3) Concerning the boundaries at infinite distance (gravity tends to 0), FEM is not well suited. I have seen on the web that some people have worked on the subject, but it is not simple (I seem to recall, for example by creating a new kind of mesh)