Error : ArityMismatch: Applying nonlinear operator Abs

Your code is much too long for me to look in detail. See for example how to create a MWE.

At a glance of the error message though it looks like you’re trying to solve a nonlinear problem as if it were linear. Somewhere you’re probably computing abs(u) where u is a ufl.TrialFunction or ufl.TestFunction. Clearly this doesn’t make sense and likely the reason you get the error.