Compute norm of assembled derivative

[LeeLizuoLiu]

I may want to know, whether there is a way to compute the norm of the assembled derivative? I tried norm(assemble(derivative(inner(grad(v), grad(v))*dx, w)), it doesn't work.

         > OK here's a significantly more minimal case. This extracts the failing operation from the adjoint, so we're now down to a failing assemble with no adjoint aspect.

from firedrake import *

n = 4
mesh = UnitSquareMesh(n,n)
V = VectorFunctionSpace(mesh, 'CG', 1)
R = FunctionSpace(mesh, 'R', 0)
# R = FunctionSpace(mesh, 'CG', 1)  - works if you use a "normal" function space
W = V*R
w = Function(W)
v, lamb0 = split(w)
assemble(derivative(inner(grad(v), grad(v))*dx, w))

Originally posted by @LeeLizuoLiu in https://github.com/firedrakeproject/firedrake/issues/2830#issuecomment-2187540974

[connorjward]

My suspicion is that it is something to do with the fact that the input to norm(...) here is a Cofunction instead of a Function and hence there may be mathematical reasons why this doesn't work.

@colinjcotter @pbrubeck do either of you know?

[colinjcotter]

Yes, the derivative is a cofunction not a function. Cofunctions have norms, obtained by Riesz map to function and then taking norm of the corresponding function.

---

From: Connor Ward @.> Sent: 26 June 2024 10:07 To: firedrakeproject/firedrake @.> Cc: Cotter, Colin J @.>; Mention @.> Subject: Re: [firedrakeproject/firedrake] Compute norm of assembled derivative (Issue #3651)

My suspicion is that it is something to do with the fact that the input to norm(...) here is a Cofunction instead of a Function and hence there may be mathematical reasons why this doesn't work.

@colinjcotterhttps://github.com/colinjcotter @pbrubeckhttps://github.com/pbrubeck do either of you know?

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[LeeLizuoLiu]

Thanks, do I need to derive the Riesz map manually?

[colinjcotter]

No, it is a method of Cofunction

On 26 Jun 2024, at 17:04, Lizuo Liu @.***> wrote:



Thanks, do I need to derive the Riesz map manually?

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[LeeLizuoLiu]

Great, thanks! I successfully implemented it.