derivative of a nonlinear form

Question

Hallo,
I have a form a=inner(q(u)*grad(u),grad(v))
with u Trialfunction and v Testfunction. Now I want to calculate the derivative of a with respect to u.
In a second step I want to evaluate this function at a function u_k (from an iterativ solve).
Is this possible with fenics?
Thanks for you help!

Comments

Please could you use the proper formatting?

Answer 1

Yes, but u should be a Function rather than a TrialFunction.

So (untested) suggestion:

u = Function(V)
v = TestFunction(V)
F = inner(q(u)*grad(u),grad(v))*dx
a = derivative(F, u)
u_k = Function(V)
b = replace(a, {u: u_k})