### Function Space for Parameters

Dear FEniCS Community,

I would like to implement a continuation method in FEniCS.

To archive this, I try to define the expanded functional \( G( \mathbf{u}, \lambda ) = ( F( \mathbf{u}, \lambda ) , f( \mathbf{u}, \lambda ) )^T\) directly in FEniCS and use the implemented nonlinear solver to solve for the PDE solution and the parameter simultaneously, instead of implementing the Newton iteration myself.

But since \(\lambda \in \mathbb{R}\) is not a function defined on the mesh, but a real number, I was wondering, if there is any way to create a function space like \( V_h \times \mathbb{R} \).

I may could use **MultiMesh** and a weird one triangle mesh to get a pure one dimensional space. But I would prefer to avoid this workaround.

If there is no nice solution, I would just implement the Newton iteration explicitly.

Kind regards,

Steffen

Cool, thanks for pointing me to defcon! That's a nice project, also mathematically. Maybe I can use defcon directly :)

Right now, I wasn't able to find in the sources how to define the function space like desired.

As far as I could look through, the newton solver is always applied for constant parameter and the parameter update is done in line 45 of defcon/parametertools.py.