Thank you Professor Bangerth for the answer! I appreciate your link to the
video a lot. And thank you for the kind words - I'll try to work harder to
match your expectations and one day contribute to deal.II :)
Have a great one,
Shawn
On Monday, April 2, 2018 at 1:22:42 PM UTC-7, Wolfgang Bangerth wrote:
>
>
> > In the step-3 example
> > (https://www.dealii.org/8.4.1/doxygen/deal.II/step_3.html), I noticed
> > that at first the variable phi is used as a test function. It is in the
> > same space with u, except for that the value is 0 on the boundaries. (in
> > this problem the boundary values for u is also 0, but it could be
> > non-zero for general cases)
> >
> > However, later, the variable phi is also the shape function. I am lost
> > in this step in understanding why the test function could be the shape
> > function at the same time. For example, if the boundary conditions of u
> > is non-zero, we'd have to have a shape function to be non-zero at the
> > boundary (right?) but the test function space needs to be 0 on the
> boundary.
>
> Your question shows a much deeper mathematical understanding of how
> strong boundary conditions actually work than most of us actually have :-)
>
> While you are correct that one can solve the problem as you suggest,
> deal.II tries to separate the treatment of boundary conditions from the
> treatment of assembly. We like to do things in such a way that we can do
> the exact same thing on each cell during assembly, without having to
> wonder whether some of the degrees of freedom are at the boundary. We
> then only later modify the resulting linear system so that it reflects
> the boundary conditions. You may want to watch lectures 21.6 and 21.65
> here
>http://www.math.colostate.edu/~bangerth/videos.html
> where I discuss exactly these sorts of issues and how they are done
> algorithmically.
>
> Best
> W.
>
>
> --
>
> Wolfgang Bangerth email: bang...@colostate.edu
>
> www: http://www.math.colostate.edu/~bangerth/
>
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