[firedrake] Projecting CG1 function into DG0 function

[Justin Chang]

Yeah I found out about errornorm recently. Have been using that now.

But as for the original issue... would D.assign(assemble(div(q) * e * dx)
suffice?

On Fri, Nov 13, 2015 at 8:27 AM, David Ham <David.Ham at imperial.ac.uk> wrote:

>
>
> On Thu, 12 Nov 2015 at 21:48 Justin Chang <jychang48 at gmail.com> wrote:
>
>> Hi guys,
>>
>> So I was attempting to do something similar:
>>
>> L2_error_norm = norm(assemble(v*(u-u_exact)*dx)/assemble(v*dx))
>>
>> where v is test function, u is FE solution, and u_exact is the analytical
>> solution. All of which are CG1 space. I get an error saying
>> "fl.log.UFLException: Division by non-scalar is undefined"
>>
>> Know what's up?
>>
>
> Yes, that's either a missing feature or a bug depending on how you look at
> it. However I think you are just confused in what you are trying to do.
>
> What you probably meant was:
>
> errornorm(u, u_exact)
>
> (errornorm is a Firedrake-provided function).
>
> What errornorm is basically doing is:
>
> assemble((u-u_exact)**2*dx))**0.5
>
> Note that this is a zero-form (no test or trial function; the answer is a
> scalar) so there are no solves, or divisions by lumped mass.
>
> errornorm actually does somewhat more sophisticated things such as
> increasing the polynomial order of the functions in order to avoid certain
> sorts of error,  so it's typically better to use errornorm than to do it
> yourself.
>
> Regards,
>
> David
>
>
>
>>
>> Thanks,
>> Justin
>>
>> On Thu, Nov 12, 2015 at 4:33 AM, Lawrence Mitchell <
>> lawrence.mitchell at imperial.ac.uk> wrote:
>>
>>> On 12/11/15 11:27, Justin Chang wrote:
>>> > David,
>>> >
>>> > So if D.assign(assemble(div(q) * e * dx)/assemble(e * dx)) returns
>>> > cell-wise div(q), what's the denominator "/assemble(e * dx)" for?
>>>
>>>
>>> It's just the normal FE L2 projection:
>>>
>>> you want:
>>>
>>> u = div(q)
>>>
>>> So you hit both sides with a test function and integrate:
>>>
>>> u*e*dx = div(q)*e*dx
>>>
>>> Where u is a trial function in DG0, e is a test function in DG and q
>>> is in whereever.
>>>
>>> But, as David points out, the DG0 mass-matrix is completely diagonal.
>>>  The values on the diagonal are just obtained by assembling the lone
>>> test function:
>>>
>>> diag = assemble(e*dx)
>>>
>>> But now, because the matrix is diagonal, you can solve the linear
>>> system pointwise by doing a pointwise division:
>>>
>>> rhs = assemble(div(q)*e*dx)
>>>
>>> solution = assemble(rhs/diag)
>>>
>>>
>>> Cheers,
>>>
>>> Lawrence
>>>
>>>
>>> _______________________________________________
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>>> firedrake at imperial.ac.uk
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>>>
>>>
>>
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