Derivative function has no attribute 'subs'

variational formulation
2

Note that F is a variational formulation (symbolical) written in the UFL form language.
To replace a coefficient in a ufl-form, you need to use ufl.replace. i.e.

from ufl import replace

F_ = replace(F, {y:y_new})

Note that this returns a ufl-form, a symbolical representation of F. To get a numerical value, you need to assemble it:

F_assembled = assemble(F_)

This returns a dolfin.Vector which you can take the norm of:

F_norm = F_assembled.norm("l2")

For your specific problem, this would end up as:

from ufl import replace
while  assemble(replace(F, {y:y_new})).norm("l2") >1e-6:
     # Add code

The same hold for this assignment, you need to use replace and assembly.

Please also note that you are constantly reassigning values in your loop.
You should use the assign function :

y_new = Function(V)
y_new.assign(project(y_BC, V))
while ...:
      if i!=0:
          y_initial.assign(y_new)
     y_new.vector()[:] = y_initial.vector()[:] - assemble(.....)[:]

Note that J is not defined outside of W(y).

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