[petsc-users] mathematics formula of DMPlexProjectFunction

[Jed Brown]

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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