Those arriving at the step-20 tutorial from step-6 (following the video
lectures) can be taken by surprise by the above statement (since this
may be a big jump in concepts to be understood). I know that this is not
the responsibility of the library to impart the theoretical knowledge,
but among the user community here, can someone point to a quick
reference to a webpage or lecture slides that mathematically shows that
the standard discretizations are not locally conservative while the
proposed replacement scheme is?
It's not so easy to show that a particular scheme does *not* possess a
particular property. It is relatively easy to show, however, that the
discontinuous pressure chosen in step-20 yields local conservation. It's
also not hard to see where the proof breaks when using Q_k elements for
the pressure, though that really only shows that the *proof doesn't
work*, not that the theorem is wrong for Q_k elements. Regardless, how
about the following:
https://github.com/dealii/dealii/pull/9478
As a side note, I think that it's true that the documentation shouldn't
replace a numerical analysis course. But I think we've also in the past
used these tutorial programs as introductions to numerical methods and
as educational tools that go beyond the immediate goal of teaching
deal.II. Since "local conservation" is an important enough concept, I
think we can devote two paragraphs to it.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to dealii+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/dealii/4370d32f-4943-9551-d096-2338f777f6a6%40colostate.edu.
