Solve a PDE coupled to an algebraic equation in Fenics

General
1

Dear all,
I looked up this topic on this forum, I only found this post, which provided no answer.

Please consider the following minimal example: a PDE for the function u({\bf x}) coupled to an algebraic equation to the variable \theta:
\nabla^2 u = f({\bf x}, \theta) \text{ on } \Omega
u = u_0 \text{ on } \partial \Omega
\theta = g(\int_{\Omega} d{\bf x} u)

I know how to solve the PDE in Fenics and how to solve the algebraic equation, for example, in python. Is there a way to solve both at the same time in Fenics, without going through an iterative solution of the PDE for multiple values of \theta?

Thank you

2

It seems to be a case for real elements. You can find an example on the scifem page and there are several discussions on this forum too.

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