On 11/30/2016 10:38 AM, Hamed Babaei wrote:
I am considering Periodic Boundary Condition for a problem which is very
simillar to step-25. Before applying periodic condition, I considered
homogeneous Newmann Boundary condition in external surfaces by simply omitting
Neumann term in week formulation (v , n.grad(u) )=0. However, since Neumann BC
has meaning when we have external surface and now I have periodicity
condition, It seems I can not have both periodic and neumann BC
simultaneously. Therefore I am going to eliminate Neumann condition by keeping
the term (v, n.grad(u)) in my right hand side as a generalized force term.
If the solution is periodic, let's say across the left and right sides of the
domain, then you have that
u(left) = u(right)
v(left) = v(right)
n(left) = -n(right)
and
grad(u)|_left = grad(u)|_right
In other words, you have that
(v, n.grad(u))_{Gamma_left} = - (v, n.grad(u))_{Gamma_right}
and consequently (if left/right are the only periodic parts of the boundary)
(v, n.grad(u))_{Gamma_periodic)
= (v, n.grad(u))_{Gamma_left} + (v, n.grad(u))_{Gamma_right}
= 0.
That means that the term you have should not appear in the bilinear form.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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