[firedrake] Projecting CG1 function into DG0 function

[Justin Chang]

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?

Thanks,
Justin

On Thursday, November 12, 2015, David Ham <David.Ham at imperial.ac.uk> wrote:

> If you're worried about performance, then you can notice that the LHS
> matrix is diagonal (because D is in DG0) so you can avoid matrix assembly
> and solve with:
>
> D.assign(assemble(div(q) * e * dx)/assemble(e * dx))
>
> (ie just divide by the diagonal entries of the matrix).
>
> On Thu, 12 Nov 2015 at 11:08 David Ham <David.Ham at imperial.ac.uk
> <javascript:_e(%7B%7D,'cvml','David.Ham at imperial.ac.uk');>> wrote:
>
>> Basically:
>>
>> d = TrialFunction(D.function_space())
>> e = TestFunction(D.function_space())
>>
>> solve(d * e * dx == div(q) * e * dx, D)
>>
>> One might have to think a little about what value this gives at the
>> boundary, but I think it's OK.
>>
>> On Thu, 12 Nov 2015 at 11:00 Justin Chang <jychang48 at gmail.com
>> <javascript:_e(%7B%7D,'cvml','jychang48 at gmail.com');>> wrote:
>>
>>> Hi all,
>>>
>>> Perhaps this may be a simple question, but say I have this bilinear and
>>> linear form:
>>>
>>> a = grad(u)*D*grad(v)*dx
>>> L = F*v*dx
>>>
>>> where u,v is trial/test function on CG1 space, and D and F are
>>> coefficients that live in DG0 space.
>>>
>>> Say I have a velocity vector function q (CG1) on the same mesh and want
>>> D to be the element-wise divergence of said velocity.
>>>
>>> How would I formulate D in Firedrake?
>>>
>>> Thanks,
>>> Justin
>>>
>>
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