Dear Wolfgang, I spent some time re-reading the theory and you are right, nothing shows that the convergence rate should be conserved when we have stabilized equal order elements. However it is interesting to note that when we use stabilization and we revert to LBB stable elements (Q2-Q1 for instance) the right order is recovered.
It seems that Richard was expecting that the order would be conserved however when PSPG stabilization is used. In our case, at least,I do not manage to reproduce that (and that is across the usage of two codes using GLS implementations). On Wednesday, 11 March 2020 12:43:18 UTC-4, Wolfgang Bangerth wrote: > > 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. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/9ef3def6-ce41-4787-9294-5e47c913b927%40googlegroups.com.
