I want to solve an equation on a 1D mesh with n elements from 0 to X. For each node of the mesh there is another equation that is solved on a 1D mesh from 0 to Y. The equations are coupled by the point values at y = Y. For example consider following simplified problem:
I already solved the problem with a segregated approach where I first solve for u and then for all c. After some iterations I get a good solution. However, I would also like to solve it fully coupled. For the real problem c also depends on u, so it is not possible to simply solve all c first and then u.
My question is if it’s possible in FEniCS to build the f vector so that it gets updated during the solution process. I already tried simply using c(Y) in the variational problem formulation but then I get following error:
ufl.log.UFLException: This integral is missing an integration domain.
Has somebody an idea how this could be done?