[firedrake] Projecting CG1 function into DG0 function

[Andrew McRae]

Is 'norm' some symbolic UFL thing?

On 12 November 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?
>
> 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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>>
>
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