> > I don't support this idea. If you take the Taylor-Green vortex for > example, the velocity decays with exp(-2 nu t), while the pressure > decays with the square of that term. Why do you expect error from your > pressure-correction scheme and your error from the time discretization > to converge in the same way? Note that they are not completely > independent of course.
The assumption was naive on my part. I had not considered that the pressure-correction scheme could introduce such a strong spatial dependency on the error saturation of the pressure field alone. I am not convinced that this completely eliminates all influence of > the pressure-correction scheme. I assume that it still gives an O(dt) > additional error (or maybe something higher order depending on your > scheme). > Yes, you are right. If those factors would reduce/eliminate the influence of the pressure-correction scheme, the Guermond problem would then showcase a lower convergence order and/or faster saturation than the Taylor-Green vortex, which is not the case. Am Sa., 24. Okt. 2020 um 17:19 Uhr schrieb Timo Heister <heis...@clemson.edu >: > > From my understanding, the lowest bound of the error on each norm is set > either by the spatial or the temporal discretization. I was kind of > expecting that the L2- and H1-Norms share a similar spatial and time > dependence, i.e. that each field reaches its lowest bound simultaneously, > and that they do so with a similar convergence rate evolution. Stated > differently, they start with an order of convergence which remains constant > for a given time step range. After reaching a small time step size, the > convergence order tends to zero as the lowest bound of the error is reached. > > I don't support this idea. If you take the Taylor-Green vortex for > example, the velocity decays with exp(-2 nu t), while the pressure > decays with the square of that term. Why do you expect error from your > pressure-correction scheme and your error from the time discretization > to converge in the same way? Note that they are not completely > independent of course. > > > Furthermore, for the Taylor-Green vortex I am using periodic boundary > conditions on all boundaries which rules out the corner singularities which > plague the pressure-correction scheme. The solution in itself is smooth, so > I had not thought the error of the boundary layer could have had such an > effect on the H1-Norm. > > I am not convinced that this completely eliminates all influence of > the pressure-correction scheme. I assume that it still gives an O(dt) > additional error (or maybe something higher order depending on your > scheme). > > > > -- > Timo Heister > http://www.math.clemson.edu/~heister/ > > -- > 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 a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/0MkM-7k6tjo/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > dealii+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/CAMRj59GKEjXp0t_5EED8myCmi0pcdwjA7GgZ2mb5vL8DpDQCCA%40mail.gmail.com > . > -- 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/CAL8bY6K_wxFzQOZ5it6YZiEbo9wbv0tFNKuM4F97PGE0s4UEQA%40mail.gmail.com.
