fiat team mailing list archive

["Robert Kirby" <robert.c.kirby@xxxxxxxxx>]

I see -- we need some kind of information for assembly.
"Direct" evaluation of the functionals is not possible except for things
that rely on black-box __call__() -- point evaluation and normal components
are good, integral moments are bad.

Marie, it's fine if you want to take a stab at getting this information in
as you suggested.



On Dec 11, 2007 2:54 PM, Anders Logg <logg@xxxxxxxxx> wrote:

> On Tue, Dec 11, 2007 at 05:16:21PM +0100, Marie Rognes wrote:
> > Robert Kirby wrote:
> > > L2 projection into the finite element space.  On each element, or
> > > globally, solve
> > > ( pi u - u , w ) = 0 for a function pi u for all of the test functions
> > > in the finite element space.
> > >
> > > All you need is point evaluation on the input function u for
> > > quadrature, and the weighted values of u become the rhs of the system.
> > >
> > > We could include the function value being integrated against, but it's
> > > going to be inexact.  I see creating interpolants as quite a bit of
> > > work with little payback when the infrastructure to do projection is
> > > already in place and typically is what is required by theorems anyway
> > > ( e.g. project initial conditions for parabolic problems into FE
> space).
> >
> > But say that you want to enforce essential boundary conditions on your
> > spaces through replacing the equations in the linear system with the
> > values of the degrees of freedom on the boundary.  Then you would need
> > to know how to evaluate the degrees of freedom, right...?
>
> I think so. For right-hand sides, we could do quadrature as suggested
> or we could first evaluate the Lagrange nodes and then do a linear
> transform from the Lagrange coefficients to say the BDM coefficients.
>
> But for boundary conditions, we only know the trace of some given
> function. Then I don't see how to do either projection (quadrature) or
> evaluating Lagrange nodes and then projection. But direct evaluation
> of the functionals (like computing the normal component at a point)
> would work.
>
> --
> Anders
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