Is 'norm' some symbolic UFL thing? On 12 November 2015 at 21:48, Justin Chang <jychang48@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@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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