Thanks for writing down that text ;)
r.
On 10/23/2012 02:16 PM, Alexander Kalinin wrote:
Oh my bad, I see. Thank you Robert!
Sincerely Alec
On Tue, Oct 23, 2012 at 4:09 PM, Robert Cimrman cimr...@ntc.zcu.cz wrote:
Check out [1] - the volume force term on the right hand side should have a minus sign - it comes from the integrating by parts when deriving the weak form.
Cheers, r.
[1] http://docs.sfepy.org/doc-**devel/tutorial.html#the-weak-** form-of-the-poisson-s-equationhttp://docs.sfepy.org/doc-devel/tutorial.html#the-weak-form-of-the-poisson-s...
On 10/23/2012 12:17 PM, Alec Kalinin wrote:
Hello SfePy,
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.
Sincerely, Alec