So... I've been working with the NonlinearImplicit system... solving
jacobian free problems using Petsc SNES.  Everything is going pretty
well (Ben's interface is great!)... but I've hit a bit of a snag on
the boundary conditions.  I would really like to impose both Dirichlet
and Neumann conditions similarly... by integrating their residual
contributions over the boundary.  So for instance for a Dirichlet
condition I have something like this:

Intg_boundary( u - BC )

and similarly for Neumann:

Intg_boundary( grad_u - BC )

The trouble that I'm running into is that these residual contributions
seem to be too small... and are only very loosely satisfied by SNES.
For instance, solving u''=0 on [0,1]x[0,1] with u=0 at x=0 and u=1 at
x=1... I end up with u actually being .3333 at x=0 and .6666 at x=1.
Of course I can dial down the residual tolerances for snes... but this
only gets me so much closer.  The other thing I've tried is to put a
multiplier in front of the boundary integral (like 1e7 or so)... this
ends up working well for satisfying the boundary conditions... but
then the interior residuals are swamped out... meaning they aren't
well resolved.

So, I'm wondering if anyone has any better ideas?  Is there a good way
to choose the correct multiplier?  Am I going about the whole thing
incorrectly?

Thanks for any help...

Derek

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