Hi all,

The problem i’m trying to solve is:

\nabla( \nabla u^2) = 0

u = 1 on \delta \Omega

This is my implementation:

```
from fenics import *
mesh = UnitIntervalMesh(10)
V = FunctionSpace(mesh, "CG", 1)
u = Function(V)
v = TestFunction(V)
dt = Constant(0.1)
theta = u**2 # scaling
F = dot(grad(theta), grad(v))*dx
bcs = DirichletBC(V, 1, "on_boundary")
solve(F==0, u, bcs)
```

The above code diverges:

```
No Jacobian form specified for nonlinear variational problem.
Differentiating residual form F to obtain Jacobian J = F'.
Calling FFC just-in-time (JIT) compiler, this may take some time.
Calling FFC just-in-time (JIT) compiler, this may take some time.
Solving nonlinear variational problem.
Newton iteration 0: r (abs) = 1.414e+00 (tol = 1.000e-10) r (rel) = 1.000e+00 (tol = 1.000e-09)
Newton iteration 1: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 2: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 3: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 4: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 5: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 6: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 7: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 8: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 9: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 10: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 11: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 12: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 13: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 14: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 15: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 16: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 17: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 18: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 19: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 20: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 21: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 22: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 23: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 24: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 25: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 26: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 27: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 28: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 29: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 30: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 31: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 32: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 33: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 34: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 35: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 36: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 37: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 38: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 39: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 40: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 41: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 42: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 43: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 44: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 45: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 46: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 47: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 48: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 49: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Newton iteration 50: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Traceback (most recent call last):
File "mwe_scaling.py", line 18, in <module>
solve(F==0, u, bcs)
File "/usr/local/lib/python3.6/dist-packages/dolfin/fem/solving.py", line 220, in solve
_solve_varproblem(*args, **kwargs)
File "/usr/local/lib/python3.6/dist-packages/dolfin/fem/solving.py", line 266, in _solve_varproblem
solver.solve()
RuntimeError:
*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
*** fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error: Unable to solve nonlinear system with NewtonSolver.
*** Reason: Newton solver did not converge because maximum number of iterations reached.
*** Where: This error was encountered inside NewtonSolver.cpp.
*** Process: 0
***
*** DOLFIN version: 2019.1.0
*** Git changeset: 74d7efe1e84d65e9433fd96c50f1d278fa3e3f3f
*** -------------------------------------------------------------------------
```

Any idea how to solve this problem?

Cheers

Remi