How would one go about solving an ODE that depends on the solution of a PDE directly in FEniCS? Is it even possible? For example, is it possible to solve $$ \partial_{t} u - \nabla \cdot (\nabla u) = f(s), \ \partial_{t} s = -g(u) \, s. $$
Hi, it is possible, cf. CBC.Beat for example.
Thanks for the reference!