[dune-pdelab] Strongly and weakly imposed boundary conditions

[Felix Heimann]

Hi Christian,

to realize standard (or strong) Dirichlet boundary conditions in PDELab,
you have to set the corresponding degrees of freedom to the values
defined by the Dirichlet condition (typically done via a call of
Dune::PDELab::interpolate(..) or automatically done by the one step
method ). Afterwards you have to tell the grid operator, that these
degrees of freedom are constrained (typically done by a call of
Dune::PDELab::constraints(..) ). There are multiple examples for this in
the pdelab-howto. If you are working with a non-trivial
GridFunctionTree, then consider especially the examples for the
Navier-Stokes equations. 

If you think it is reasonable to do so, you can in principle use a
different function for the interpolate call than you pass to the local
operator as "weak-Dirichlet" boundary function.

To find out which boundary condition is to be used where you have to use
a indicator function. Here you definitely use always the same function.
There are various examples for this too in the pdelab-howto (also see
the Navier-Stokes example).

I am not really sure I got your point, so feel free to elucidate...

Best Regards,
Felix

Am Mittwoch, den 05.10.2011, 08:21 +0200 schrieb Christian Simon:
> Dear Duners,
> 
> in order to implement boundary conditions for a multiphase formulation
> in Dune-pdelab,
> I have to use strongly and weakly fulfilled boundary conditions. I
> implemented the weak
> Dirichlet-bc in the alpha_boundary method by extracting them from a
> boundary function. 
> 
> My question now is: How can I take the strong Dirichlet bc from
> another bc- function 
> into account? I thought, I should use them in the solver call "apply",
> but I can't use 
> only the strong bc, because I have to consider the structure of the
> GridFunctionTree, 
> is that right?
> In other words: How can I combine strongly and weakly fulfilled
> Dirichlet bc in my set 
> of boundary conditions in order to pass it to the apply method of the
> solver?
> 
> Thanks in advance, 
> Christian Simon
> 
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-- 
Felix Heimann
Universität Heidelberg
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