Defining u_z = u_xx+u_yy

Question

I have a 3D domain ( a box) , on which I'm trying to solve the following PDE

$
u_z = u_{xx} + u_{yy}
$

All FeniCS demos use a PDE, which has the full Laplace operator $\Delta u$ or the full gradient $\nabla u$ in it, and in my example I need to separate all variables, because I take fist derivative with respect to $z$ , and second derivatives with respect to the other variables $x$ and $y$.

How do I define in Fenics derivatives with respect to ${x,y,z}$ separately ?

I mean I would like to code something like

inner(xderivative(u), v) * dx
inner(yderivative(u), yderivative(v)) * dx

Comments

You need to show that you've done due diligence in first looking at demos, and then ask a specific FEniCS question. You'll then be more likely to get an answer.

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Ok, I modified the question a bit, I cannot find in any of the demos what I need.

Answer 1

Maybe you should take a look at this, section 5.6. and create your own operator.
http://fenicsproject.org/pub/documents/ffc/ffc-user-manual/ffc-user-manual.pdf

Answer 2

xderivative(u) = u.dx(0)
yderivative(u) = u.dx(1)
and so on ..