On 3/11/20 8:54 AM, Bruno Blais wrote:
Q1-Q1 using the GLS (SUPG +PSPG) stabilized solver of Lethe using a
monolithic iterative solver and Q2-Q1 using the Grad-Div solver with a
Schur completement solution strategy (similar to step-57 but using
Trilinos).
*Here are the results I obtain:*
*Q1-Q1 - Velocity error and convergence*
cells error
64 1.3282e-01 -
256 3.4363e-02 1.95
1024 8.7362e-03 1.98
4096 2.1969e-03 1.99
16384 5.5029e-04 2.00
65536 1.3767e-04 2.00
262144 3.4426e-05 2.00
1048576 8.6075e-06 2.00
/Conclusion : Order = p+1 recovered for the velocity!/
*Q1-Q1 - Pressure error and convergence*
Refinement level L2Error-Pressure Ratio
1 0.171975
2 0.0964683 1.33
3 0.0301739 1.78
4 0.00844618 1.89
5 0.0023758 1.885
6 0.000698421 1.84
7 0.000216927 1.79
8 7.07505e-05 1.75
/Conclusion : Order = ??? The error does not reach the right asymptotic
convergence rate./
If I understand the chain of emails correctly, this is the question you
have: Using a Q1/Q1 element with GLS/PSPG, what convergence rates does
one expect.
You seem to suggest that it should be 2 for both velocity and pressure.
But is that true? What does the theory say? I would actually be quite
surprised if that's what you get for these kinds of problems. My gut
feeling is that you should expect 2=p+1 for the velocity, but something
between p and p+1 for the pressure. That would be consistent with other
stabilized approaches.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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