May be I am wrong, but it seems that there is an issue with the minus sign
before volume integral in Poisson problem definition.
I am trying to solve Poisson problem for the simple analytical function
$u(x) = x^2$, so the $\Delta u = 2$ and the week form is $\int_\Omega u v
\, d\Omega = \int_\Omega 2 v \, d\Omega$.
In SfePy I used the following definition:
dw_laplace.i1.Omega(m.val, v, u) = dw_volume_integrate.i1.Omega(f.val, v)
but I got a quite big relative error: 1e-1
But in case I add the minus sign:
dw_laplace.i1.Omega(m.val, v, u) = -dw_volume_integrate.i1.Omega(f.val, v)
the accuracy of the solution becomes very good, the relative error: 1e-3
So my question, why it is necessary to add minus sign before volume
integral? Yes, I know that the classical Poisson problem is $u(x) = -f(x)$.
May be we assume minus sign implicitly?
The test script demonstrated a problem is in the attachment.