[petsc-users] mathematics formula of DMPlexProjectFunction

[Fande Kong]

Jed, Thanks.

It means that the inner product against basis "n_i" is just the function
value at the point "x_i" if the function is sufficiently regular, e.g.,
sin(x) or cos(x).

The basis function at x_i is "x-x_i" which is not the one we use
to discretize the equations?


On Tue, Oct 20, 2015 at 12:03 PM, Jed Brown <jed at jedbrown.org> wrote:

> Fande Kong <fdkong.jd at gmail.com> writes:
> > Any body knows the mathematics formula corresponding to the function
> > DMPlexProjectFunction? I already went through the code, but I do not
> > understand quite well. I will appreciate any help.
>
> The definition of a finite element involves a dual space (the basis for
> which is sometimes called the "nodes").  For a typical finite element
> space, the "nodes" are Dirac delta functions at vertices.  Consequently,
> the inner product
>
>   (n_i, f) = \int \delta(x - x_i) f(x) = f(x_i)
>
> if f is sufficiently regular.  For more general dual basis functions,
> this inner product needs to be evaluated by quadrature.
> DMPlexProjectFunction does this projection.
>
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