Explanation of right hand side in example 33?

[Maxi Miller]

I try to follow the math in example 33, but am not fully able to understand how the right hand side is included. According to my understanding, I have the function/vector G, multiply it with the test function z, and integrate over both over the whole area. After there are no derivatives included, I do not have to do any reformulations. Why do I then still end up with an integral over both (G\cdot z), but integrated over the border?

Thanks!

[Wolfgang Bangerth]

Can you point out where in the code this happens?

There is of course a boundary term that comes from integrating by parts the
equation. But G itself should not appear in a boundary integral.

Best
W.

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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Maxi Miller]

I refer to the part where the spatial residual is defined as B(w_n)(z)=...

There you integrate over G(w_n), z over \partial\Omega, but I would have expected to integrate over \Omega. I have not compared that equation with the code yet, after I already had problems with that step.

[Wolfgang Bangerth]

On 08/16/2017 07:43 AM, 'Maxi Miller' via deal.II User Group wrote:
> I refer to the part where the spatial residual is defined as B(w_n)(z)=...
> There you integrate over G(w_n), z over \partial\Omega, but I would have
> expected to integrate over \Omega.

Yes, this looks wrong. A patch is here:
https://github.com/dealii/dealii/pull/4876
Thanks for pointing it out!

> I have not compared that equation with the
> code yet, after I already had problems with that step.

I suspect that it was just the formula that was wrong, and not the code, given
that it was so obvious. But take a look, and if you find anything you don't
understand about the code, ask again!

Thanks