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Problem with L2 Norm of stress for a plate with circular hole

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Old   September 28, 2022, 11:01
Default Problem with L2 Norm of stress for a plate with circular hole
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Yusuf Elbadry
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Hello!
I have having a problem with calculating the L2 Norm of stress and displacement. I am solving a plate with a circular hole using IGA. I am using an open-source package called NLIGA (written in MATLAB). I am solving the upper right quarter of the problem with symmetric BC on the left and bottom boundaries and tension on the right and upper boundaries.


I calculated the Energy norm and it converges well (0.5*u'*K*u).
But for calculating
|| u_app - u_ex ||_L2
and
|| sigma_h - sigma_ex ||_L2

The behavior is not expected at all and I tried to compare it with T.J.R Hughes's paper (2005).

For the L2 norm of stress, for example, I tried calculating it at p=q=2 and p=q=3 and plotting it on log-log with "total number of elements" as the horizontal axis. I am expecting to see a line for each degree with a negative slope. What I got for each case is a line with a negative slope but somehow the L2 norm converges to a value! lets say 0.0508. So, both L2 norms at different polynomial degrees, reach the same value at the end.

Is there any explanation for that?!!!
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