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

[Geoffrey Irving]

On Fri, Jan 17, 2014 at 3:29 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Fri, Jan 17, 2014 at 4:09 PM, Geoffrey Irving <irving at naml.us> wrote:
>>
>> Do the test functions we integrate against to form residuals with
>> PetscFE come from the primal space or the dual space?  I.e., is
>> PetscFE always Galerkin?  If it isn't always Galerkin, when would it
>> be?
>
>
> They come from the dual space. I do not think I have made any assumptions
> that prevent Petrov-Galerkin, but I have also never tried an example.
>
> You can see the code that does tabulation here:
>
> https://bitbucket.org/petsc/petsc/src/cdce425498f34eac2bb744f37c9fe1bd5a97b9d8/src/dm/dt/interface/dtfe.c?at=master#cl-2317

Thanks.  To confirm: the default thing as set up in ex12 is Galerkin,
meaning that the primal and dual space basis functions are identical?
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.

Geoffrey