Action of the time derivative

variational formulation
1

Hey guys, I’ve been looking a bunch of questions about derivatives and I couldn’t find anything useful to the problem I am dealing at the moment. If there is already an answer please leave the link for me.

Well, I would like to know if there is a way to compute the action of the time derivative of a trial function u on a teste function v. I am solving a parabolic type equation and I don’t want to use a finite difference approach to deal with the time derivative. I am dealing with time as a third coordinate (meaning u(x,y,t)) and I need to implement the term \langle u_t,v\rangle in my variational formulation \langle u_t,v\rangle + (\nabla u,\nabla v) = (f,v). Does anyone know a way to do that on Fenics?

Thanks in advance!!!

2

I think you can write

u_t = u.dx(2)

Similar to Derivative term in only one direction - #4 by bleyerj

3

That means that \langle u_t, v\rangle can be written as

u.dx(2) * v * dx

?