Hi,
I would like to know if it’s possible to solve an algebraic equation coupled to a differential equation, considering the case where the algebraic equation is a relation between unknown nodal values.
As an example, consider the following equations:
-\int_0^L v'u'dy+\lambda\int_0^L v dy=0
\sum_iu_iu_i+\lambda^2=1
where, u and v are the trial and test functions, respectively, \lambda is an unknown scalar value, and u_i represents the nodal value of u.
I am wondering if it possible to solve this type of system using fenics. If in the second equation, rather than a summation term there was some integral relation with the field u, I could just define \lambda using a Real function space. However, I am uncertain about the appropriate approach to take in this case.
If you could provide me with any insights or suggestions regarding how I might be able to solve this problem, I would greatly appreciate it.
Thanks in advance.