*"We do the same on the velocity. That's why we integrate by parts the form"*
Thank you so much for clarifying. That explains it, and I now understand this fully. The original sentence was a bit misleading. "In practice, one wants to impose as little regularity on the pressure variable as possible". For someone who hasn't studied fluid dynamics, it can potentially plant doubts in one's head to mean something like: *"Perhaps there exists some special mathematical considerations informed by the physics of the pressure variable that requires it be as less regular as possible, and therefore maybe some extra work and careful thought is needed specifically for this problem, which is somehow different from all others studied in tutorials so far". * I shall now de-emphase this in my mind and take this sentence to mean as* "In practice, one wants to impose as little regularity on the pressure variable as possible (just like every field variable solved by the Galerkin method in every tutorial thus far)".* Thanks a lot once again for the clarification. Apologies for asking such basic questions. Regards, Krishna On Wednesday, March 11, 2020 at 9:20:56 PM UTC, Wolfgang Bangerth wrote: > > On 3/10/20 12:59 PM, Krishnakumar Gopalakrishnan wrote: > > Step-22 has a strong-sounding stub-like statement:/"In practice, one > > wants to impose as little regularity on the pressure variable as > possible". > > / > > / > > / > > The above one-liner (fairly enough) assumes domain knowledge. As a new > > entrant to deal.ii (haven't studied fluid mechanics before), may I ask > > the following? > > > > 1. Why do we impose as little regularity on the pressure as possible? > > We do the same on the velocity. That's why we integrate by parts the form > \int v (-Delta u) > to > \int \nabla v . \nabla u > > > > 2. When I attempt to solve my own PDE (outside traditional areas such > > as fluid or structural mechanics), what properties should I know > > about the field variable to correctly apply the procedure and > > learnings from this tutorial, i.e. what exactly is the regularity > > condition mentioned here? > > You'll have to take a second course on PDEs, and most importantly learn > a bit about the theory of weak solutions. Here's a patch that explains > this in about as much detail as I would like to go into: > https://github.com/dealii/dealii/pull/9652/files > > 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/dbb1c13c-6d02-42f4-a6c0-7689c5ba321a%40googlegroups.com.
