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On 23/04/18 21:10, Eric M wrote:
> revision:
> I put gx in VGrad as well. My outputs are as expected.
> Though it seems slightly strange to have what should be an exact
> function (gx) interpolated to a discontinuous space.

See below.

> On Mon, Apr 23, 2018 at 2:51 PM, Eric M <eric.malitz@gmail.com

> <mailto:eric.malitz@gmail.com>> wrote:
>
>         Aha, there is a confusion here between what is a coefficient
>         in some finite element space, and what is a symbolic expression.
>         You start with u, which is a Function in some finite element
>         space.
>         Now grad(u)[0], or u.dx(0) (these actually produce the same
>         thing) are symbolic expressions.
>         If you want to look at the values, you first need to
>         interpolate (or project) the expression into a suitable finite
>         element space:
>         e.g, if u is in FunctionSpace(mesh, "CG", 2)
>         Then perhaps:
>         VGrad = FunctionSpace(mesh, "DG", 1)
>         gradu = project(grad(u), VGrad)
>         gradu.dat.data[:] ...
>
>
>      For an exact solution g, I have gx, it's derivative. I wish to
>     compare gx against the x derivative of a solution uk. I have:
>
>     V = FunctionSpace(mesh, "Lagrange", 2)
>     Sigma = TensorFunctionSpace(mesh, "Lagrange", 2)
>     gx=Function(V)
>     gx.interpolate(x*exp((x**2+y**2)/2))
>
>     VGrad=FunctionSpace(mesh,"DG",1)
>
>     (solve a problem, split uk from the mixed solution so uk is in V)
>
>     gradu_x=project(grad(uk)[0],VGrad) 
>
>     But now gradu_x and gx are different lengths. I see why we would
>     use this VGrad. Does it make sense to do 
>     VGrad=FunctionSpace(mesh,"Lagrange",2) instead? 

I suggested a DG space because in general the grad of some CG space is
not continuous.  But if you have some exact expression you can compare
to, then you can compute norms directly:

gx = x*exp((x**2 + y**2)/2)

L2diff = norm(gx - grad(uk)[0])

Make sense?

Cheers,

Lawrence