On 12/05/2016 04:53 PM, Hamed Babaei wrote:
Dear Daniel,
The question in the end is just how the weak formulation you are
interested in looks like and what the appropriate function spaces are.
If you are using periodic boundary conditions, you are saying that there
is no boundary but that these faces should be treated the same as internal
faces.
Hence, it sounds weird to want to do something more there regarding
boundary values. What else do you want to achieve with respect to your
formulation?
Let me repeat a question here that I asked you in another post which is
related to this discussion.
I would like to explain where is the issue. I am dealing with a problem which
is very similar to a thermoelastic problem, in which instead of temperature I
have an internal variable for phase transformation in solids which varies from
0 to 1 ( zero value for initial phase and 1 for final phase). So I solve two
equations separately, an elastic equation for displacement and an parabolic
equation for internal variable, very similar to heat equation. I have
considered periodic boundary condition for both displacement and internal
variable. However, I faced a problem with internal variable field when having
periodic condition. Ironically, although the periodic condition on pair faces
are truly applied, the internal variable at the periodic faces never reach 1.
I thought it may be due to having periodicity and Nuemann BC simultaneously
since I had eliminated the Nuemann term in the week formulation by considering
(v, n\cdot\nabla u)=0.
You can't do this. In essence you want to have a source on the boundary *and*
periodic boundary conditions. You need to drop the term.
(Mathematically, that's because along the boundary you will have a source
n.grad u from one side, and a counter-acting source from the other side where
the solution continues in a periodic manner. Just remove the term from your
bilinear form and you should be ok.)
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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