On Thu, Jan 09, 2014 at 09:00:38PM +0100, Jan Blechta wrote:
> On Thu, 9 Jan 2014 11:26:09 -0800
> Nikolaus Rath <[email protected]> wrote:
>
> > On 01/09/2014 11:19 AM, Jan Blechta wrote:
> > >> So if I understand correctly, I don't need to do anything special
> > >> for
> > >> > the boundary conditions because Dolfin assumes Neumann by
> > >> > default, and Neumann conditions are only reflected in L.
> > > This is not true - DOLFIN does not assume. It is a property of this
> > > variational problem.
> >
> > Huh? Maybe we misunderstood each other, but
> > http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/neumann-poisson/python/documentation.html
> > says:
> >
> > "Since we have natural (Neumann) boundary conditions in this problem,
> > we don´t have to implement boundary conditions. This is because
> > Neumann boundary conditions are default in DOLFIN."
>
> So this is basically wrong (probably written by some graduate
> student).
This sentence was indeed written by a student but I would not say that
it is wrong. This problem does use natural boundary conditions which
in this case are of Neumann type and for that reason, one does not
need to impose boundary conditions explicitly.
But I agree that if one just reads that single sentence it is somewhat
misleading. It does not mean one does not need to think about the
boundary conditions or take special measures to implement them
correctly. If one reads the rest of the page, there is a long
discussion on exactly this issue: which measures have to be taken to
solve the pure Neumann problem.
--
Anders
> It is a mathematical property of this particular problem. Check
> mixed-poisson demo - the situation is switched there, Dirichlet BCs are
> natural, because of mathematics, not because of DOLFIN.
>
> Natural BC (it can be Neumann (typically for second order problems,
> but dependes on the formulation) or Dirichlet or nothing or anything
> else) is BC which is not incorporated to function space (which is done
> in DOLFIN algebraically by DirichletBC) and is represented by surface
> integral (which can be zero, so one gets homogeneous condition).
>
> Jan
>
> >
> > which seems to be the same as what I said above.
> >
> > It seems to me that Dolfin could just as well use e.g. Dirichlet
> > conditions with a constant value on the boundary if no BC's are
> > specified, so how is using Neumann conditions in this situation
> > anything but an assumption by Dolfin that this what is most commonly
> > wanted?
> >
> > > However, even after going through the example, I'm not sure how I
> > > can tell FEniCS to use only trial functions satisfying Laplace's
> > > equation. In the example, the constraint on the test functions
> > > seems to fix just the constant offset. It's not clear to me to
> > > extend this to something more complicated, where the constraint
> > > itself takes the form of a PDE. Do you think you could explain in a
> > > bit more detail? You change the constraint to Laplace problem, and
> > > the space R for Lagrange multiplier and corresponding test function
> > > to some appropriate FE subspace of Sobolev space W_0^{1,2}. Hint:
> > > http://en.wikipedia.org/wiki/Lagrange_multipliers_on_Banach_spaces
> > I'll look into that. Thanks!
> >
> >
> > Best,
> > Nikolaus
> >
>
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