Different solution with different Finite Elements (Linear - Quadratic)

I would strongly suggest you elaborate on what you mean by

as it is not clear what you expect. Is the solver not converging, are your plots looking wrong etc?
Please also ready the guidlines in

on how to get your question answered, as your code is far from a minimal example.

Please also note that you are using a fixed quadrature degree,

which can cause problems for higher order spaces,as you then under-integrate the variational forms.