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.
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