Hi, I am trying to solve following time dependent nonlinear problem

where `u^j`

is the solution at `j`

th time level and `u^{j+1}`

is the solution at `j+1`

th time level. I’m stuck on define the problem in fenics. My definition for variational problem in Fenics is as follows

```
F = (inner((u - u_)/dt, v) + inner(u.dx(0)+u.dx(1),v) + inner(dot(u,nabla_grad(u)), v)+\
inner((grad(u)-grad(u_))/dt, grad(v)))*dx
```

Can you give me feedback on whether it is true. İf it is not, what is its correct form?

Thank you.