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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