### Simple question about divergence of a vector field

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I am new to FEniCS and I am trying to verify a small portion of my code that is giving me unexpected results. I am trying to verify $\Delta F=4$Δ

`F`=4 where $F=x^2+y^2$`F`=`x`^{2}+`y`^{2}. My simple code snippet is as follows:```
cells_per_side = 32
mesh = UnitSquareMesh(cells_per_side,cells_per_side)
V = FunctionSpace(mesh, 'P', 1)
F = project(Expression('x[0]*x[0] + x[1]*x[1]',degree=2), V)
plot_func(div(grad(F))
```

$F$`F` and its gradients seem to compute just fine but I get a function identical to zero for $\Delta F$Δ`F` . Is there something obvious that I am missing here?

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3

Is it because you project degree=2 to FunctionSpace P1, which seems too low in this case?

written
12 months ago by
Corwinpro

1

You might also want to use interpolate(...) instead of project(...), since projection only results in approximate values.

written
12 months ago by
Adam Janecka

Too right, too right.

written
12 months ago by
pf4d

### 1 Answer

2

Yes, the 1st derivative of the linear P1 space is constant, and the 2nd derivative is identically zero. Hence, increase the order to at least P2.
Yeah, that seemed to have been it. How silly of me. Thanks!

written
12 months ago by
Sheroze Sheriffdeen

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