Georgios,
Thanks for your reply! Essentially what I was trying to do is patch together
two product spaces: ([H1_0]^2, L^2_0) in one part of the domain and
([H1_0]^2, L^2_0) in another, with an interface condition to ensure
solvability for my problem (Stokes in one part of the domain, laplace in
another). The interface condition was chosen such that there would be no jump
of the velocity gradient across the interface (this was done by choosing an
L2_0 pressure that goes in the right-hand side).
Can you state this interface condition in mathematical terms? In general,
functions in H^1 can be expected to be continuous along interfaces, but their
gradients can not. Indeed, their normal derivatives along the interface will
only be in H^{-1/2}, and so the difference between the normal derivatives from
both sides of the interface can at best be expected to be weakly continuous
(i.e., when tested with a sufficiently smooth test function).
Unfortunately this did not
work in the implementation phase and I ended up getting a jump of the velocity
gradient across the interface.
But is this different than the jump in the gradient between each cell and the
next? There, the gradient is not continuous either. The question is what
happens as you let the mesh size go to zero.
At the moment I don't know if this is a coding
bug, or an erroneous choice of spaces. To be honest I expected weak
differentiability to be enough to ensure a zero velocity gradient jump across
the interface too. As such, I was thinking how I should choose my spaces to
ensure gradient continuity across the interface to see if this would fix my
problem but I do not know how to enforce that in deal.ii. As such, any advice
on how to do that would be great.
It's actually quite complicated to ensure continuity of the gradient strongly.
This is why the biharmonic equation is so difficult to solve!
Best
Wolfgang
--
------------------------------------------------------------------------
Wolfgang Bangerth email: [email protected]
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 [email protected].
For more options, visit https://groups.google.com/d/optout.
