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PDE problem with no Dirichlet BC

Asked by Hossein Nili

Hi

I have a (time-dependent) PDE to solve with initial conditions but no Dirichlet boundary conditions. This is probably my misunderstanding of the tutorial, but do I have to define Dirichlet boundary conditions in order to be able to solve a PDE? You see the problem is, when it comes to writing solve(a == L, u, bc), the bc argument should (?) correspond to a Dirichlet BC and if I have none, I seem not to be able to ask for a solution. Am I being very wrong here?

Many advance thanks for your help,

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Jan Blechta (blechta) said : 		#1

On Wed, 27 Mar 2013 19:26:03 -0000
Hossein Nili <email address hidden> wrote:
> New question #225298 on FEniCS Project:
> https://answers.launchpad.net/fenics/+question/225298
>
> Hi
>
> I have a (time-dependent) PDE to solve with initial conditions but no
> Dirichlet boundary conditions. This is probably my misunderstanding
> of the tutorial, but do I have to define Dirichlet boundary
> conditions in order to be able to solve a PDE? You see the problem
> is, when it comes to writing solve(a == L, u, bc), the bc argument
> should (?) correspond to a Dirichlet BC and if I have none, I seem
> not to be able to ask for a solution. Am I being very wrong here?
>
> Many advance thanks for your help,
>

At first that's question for the variational (weak) theory of PDEs if
given PDE is solvable with no Dirichlet BCs. Moreover if theory
provides well-posedness of problem with no DIRchlet BCs then it might
sometimes be necessary to introduce
  -Lagrange multiplier (neumann-poisson demo) or
  -pin point (nsbench in FEniCS book) or
  -set null space for krylov solver (singular demo)
to avoid singularity of problem.

At second solve(a == L, u) corresponds to solution with no Dirichlet
BCs.

Jan

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