# Solving a problem with only Neumann boundary conditions

Dear all

I'm trying to solve the following problem:

-d/dx(du/dx) - (du/dx)^3 = 0 on 0 < x < 1

subject to the following bcs:

@ x= 0: du/dx + u = 3/sqrt(2)
@ x = 1: du/dx = 0.5

I have in my ufl file:
L = inner(grad(v), grad(u))*dx - v*( (u.dx(0))**3 )*dx - v*((1.5*sqrt(2)-u))*ds(0) - v*(0.5)*ds(1)

I assume that ufl doesn't know about the boundaries, so in main.cpp, I have marked them like so:
MeshFunction<dolfin::uint> boundaries(mesh, mesh.topology().dim()-1);

LeftNeumannBoundary boundaryL;
boundaryL.mark(boundaries, 0);

RightNeumannBoundary boundaryR;
boundaryR.mark(boundaries, 1);

The problem is how to use the VariationalProblem class. It requires the dirichlet bc, the cell_domains, the interior and exterior_facet_domains.

How can I use VariationalProblem without specifying the dirichlet bc?

Thanks

Jack

## Question information

Language:
English Edit question
Status:
Solved
For:
DOLFIN Edit question
Assignee:
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Solved by:
Johan Hake
Solved:
2010-03-28
Last query:
2010-03-28
2010-03-28
 Johan Hake (johan-hake) said on 2010-03-28: #1

On Saturday March 27 2010 05:54:46 Jack wrote:
> New question #105698 on DOLFIN:
>
> Dear all
>
> I'm trying to solve the following problem:
>
> -d/dx(du/dx) - (du/dx)^3 = 0 on 0 < x < 1
>
> subject to the following bcs:
>
> @ x= 0: du/dx + u = 3/sqrt(2)
> @ x = 1: du/dx = 0.5
>
> I have in my ufl file:
> v*((1.5*sqrt(2)-u))*ds(0) - v*(0.5)*ds(1)
>
> I assume that ufl doesn't know about the boundaries, so in main.cpp, I have
> marked them like so: MeshFunction<dolfin::uint> boundaries(mesh,
> mesh.topology().dim()-1);
>
> LeftNeumannBoundary boundaryL;
> boundaryL.mark(boundaries, 0);
>
> RightNeumannBoundary boundaryR;
> boundaryR.mark(boundaries, 1);
>
> The problem is how to use the VariationalProblem class. It requires the
> dirichlet bc, the cell_domains, the interior and exterior_facet_domains.

Just pass boundaries as exterior_facet_domains and DOLFIN will assemble the
correct forms at the marked boundaries.

Johan

> How can I use VariationalProblem without specifying the dirichlet bc?
>
> Thanks
>
> Jack

 Jack (attacking-chess) said on 2010-03-28: #2

Thanks Johan Hake, that solved my question.

 Thomas Ward (tomwardathome-gmail) said on 2010-05-04: #3

Jack

I might be wrong but shouldn't that first BC be in the bilinear form rather than the linear?

Tom