[petsc-dev] are petscfe tests functions dual or primal?

[Jed Brown]

Geoffrey Irving <irving at naml.us> writes:
> Thanks.  To confirm: the default thing as set up in ex12 is Galerkin,
> meaning that the primal and dual space basis functions are identical?

Yes.

> If that's true, how does DMDAProjectFunctionalLocal work?  As far as I
> know DMDAProjectFunctionalLocal projects an analytically defined
> function into the primal space, but it uses the dual space to do that
> via PetscDualSpaceApply, which would imply that the dual space is
> knowable in terms of the primal space.  If the dual space can be
> either Galerkin (same the primal) or Petrov-Galerkin (different), I
> seem to be missing something.

Most Petrov-Galerkin methods use test functions that are only
modifications of the trial functions.  SUPG is the classical example,
but DPG and others are also of this form.  These are implemented by
bringing the modification into the discrete weak form, in which case
there is only one basis tabulation.

Weighted residual methods form a larger class of methods (that includes
FD and FV), for which the primal and dual spaces need to be tabulated
separately (or specialize the method).

Is there something specific you are trying to do?
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