I’m a new Fenics user and still getting used to formulating PDEs in weak form. While I understand all simple examples, there are terms that I don’t know what to do with.

For instance, let’s take a vector function that evolves like this

where \Sigma can be a stress in a NS equation. Now, if \Sigma has derivatives of other field, for instance a function like

where \phi is another field. What would be the best way of dealing with something like this in Fenics?

Since \Sigma has a second derivative, would I have to create another tensorial function space in which I solve for \Sigma? There I could solve the following weak form for a test function K_{ij}:

Is this the smartest way to solve this? Could it be done without having to use a new tensorial function space, and keeping a single weak form for u (and of course another for \phi)?

Since this is very related to nematic order parameters, are there any good Fenics examples out there for solving for nematic fields?