1D ODE - first derivative term.

[ethrelfall]

Dear community,

I want to specify the weak form of the 1D ODE $u' + (x u')' + 1 = 0$.

Once multiplied by a test function v and integrated by parts, the first term gives me $- \int u v' \text{d}x$.

How can I specify this term in Firedrake e.g. I cannot do u*grad(v) or inner(u, grad(v)) due to shape mismatch (it thinks one of the objects is a vector and one a scalar)? Note the second term in the original eq. is fine as x*inner(grad(u), grad(v)) is allowed.

I guess one way around the problem is to put the ODE into self-adjoint-like form $(p u')'+q u = \text{stuff}$ ... but what if I don't want to do that?

(Checked for matching discussions.)

Thanks!

[wence-]

UFL doesn't exploit (kind of deliberately, I think) the isomorphism between scalars, and 1D vectors. So the way round this is that you need to index the grad(v) term (or equally just take the x derivative because you know that's the only one).

So try with either u*grad(v)[0] or u*v.dx(0).

[ethrelfall]

Many thanks, that works fine!