[firedrake] Projecting CG1 function into DG0 function

[Lawrence Mitchell]

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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