On 11/22/2016 04:27 AM, Ashkan Dorostkar wrote:
Next, I produce the right-hand side of my system by computing a surface
integral. In this Integral, I integrate a constant function times a basis
function.
One expects the resulting vector to be constant but I get different values in
it.
I have visualized the right-hand side and have attached the figure here.
I have also made and attached a minimal program that produces this figure.
I don't think this behavior is correct. Does anyone have any ideas? Have I
missed anything in the implementation or otherwise?
I think your assumptions are wrong.
Imagine that you were just working on a mesh in the plane as we usually do.
Also imagine that we just used the lowest order Q_1 elements. Then, each entry
of your right hand side vector would simply be
F_i = \int_\Omega \varphi_i(x) dx
Now, \varphi_i is defined at a vertex, and the integral will only extend over
the cells that are adjacent to that vertex. Then, clearly, the F_i will only
all be equal if each vertex is surrounded by cells that are all of equal size.
This will not be the case, on the other hand, for vertices at the boundary, or
if the mesh is not composed of cells that are all of the same shape.
The latter is exactly the case with the mesh you show.
Best
W.
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Wolfgang Bangerth email: [email protected]
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