[dune-pdelab] How to impose pure Neumann boundary condition

[Peter Bastian]

Hi Jizhou,

You have to:

- Use NoConstraints (as in example01 and described by Steffen)
- Ensure the right hand side is in the range of your matrix
- Use an appropriate iterative solve (preconditioned CG should work)

To really ensure a zero mean value zero through constraints is in principle
possible but not with the current constraints assemble interface (because it
only allows you specify a constraint where one dog depends on other dogs
of the same element as in hanging nodes (for Dirichlet dofs are a special case
where a dog depends on nothing)).

We also did not implement a preconditioned that subtracts the mean value after each 
iteration but that could very easily be done, so if the suggestion above does not
work you have to do that (or add a tiny Dirichlet boundary to your problem).

Best,

Peter

Am 15.11.2012 um 18:05 schrieb Steffen Müthing <steffen.muething at ipvs.uni-stuttgart.de>:

> Hi Jizhou,
> 
> for an example, look at src/course-examples/example01a_Q1.hh in the dune-pdelab-howto module:
> As a pure Neumann space does not have any kind of built-in constraints (the Neumann
> boundary conditions enter through your weak form), just choose Dune::PDELab::NoConstraints
> as the constraints parameter for your GridFunctionSpace.
> 
> Just make sure you still end up with a well-defined problem if you don't have any Dirichlet constraints…
> 
> Best,
> 
> Steffen
> 
> 
> Am 15.11.2012 um 17:42 schrieb Jizhou Li:
> 
>> Hi,
>> I am very new to dune-pdelab. On the pdelab-howto-article page 132-133, it says dune-pdelab can handle pure Neumann boundary condition. Does anyone know how to get it done? Or just to construct finite element space with {q:  ∫q dΩ=0}. I think it would be helpful for to have an example on howto-article for beginners.
>> 
>> Thanks
>> 
>> Jizhou Li
>> _______________________________________________
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> 
> Steffen Müthing
> Universität Stuttgart
> Institut für Parallele und Verteilte Systeme
> Universitätsstr. 38
> 70569 Stuttgart
> Tel: +49 711 685 88429
> Fax: +49 711 685 88340
> Email: steffen.muething at ipvs.uni-stuttgart.de
> 
> _______________________________________________
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------------------------------------------------------------
Peter Bastian
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
Universität Heidelberg
Im Neuenheimer Feld 368
D-69120 Heidelberg
Tel: 0049 (0) 6221 548261
Fax: 0049 (0) 6221 548884
email: peter.bastian at iwr.uni-heidelberg.de
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