[firedrake] absolute value of gradient

[George Ovchinnikov]

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Hi Lawrence,

> sqrt(dot(grad(w), grad(w)))

Yes, this is exactly what I meant. I needed to use in Tikhonov
regularization in method which I'm working with.
I'm updating on every step w based on the rule
H(w) - \alpha |\grad(w)|,

where H(w) is basic updating rule, and |\grad(w)| is a penalty for
local non-smoothness.

- --George

On 18.11.2015 19:21, Lawrence Mitchell wrote:
> On 18/11/15 15:42, George Ovchinnikov wrote:
>> Hello folks,
>> 
>> I have a scalar field in 2D, $w$, say:
>> 
>> V = FunctionSpace(mesh, "CG", 1) w  = Function(V) 
>> w.interpolate(Expression("1"))
>> 
>> and I need too find an norm of grad(w) in every point of the
>> given area, i.e. get a scalar field back.
>> 
>> I've found no way to iterate through individual elements of
>> grad(w) to be able to do in manually, neither abs(grad(w)) or
>> something similar works. Any ideas? Do I need to solve some
>> variational problem for this, too?
> 
> You can't do this pointwise because the strong gradient doesn't
> exist.
> 
> What do you later want to use this for.  If you need |grad(w)| in
> a form, you can just write it in directly.  When you say norm
> grad(w), do you mean:
> 
> sqrt(dot(grad(w), grad(w))) ?
> 
> 
> Lawrence
> 
> 
> 
> _______________________________________________ firedrake mailing
> list firedrake at imperial.ac.uk 
> https://mailman.ic.ac.uk/mailman/listinfo/firedrake
> 

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