[Getdp] Neuman's problem for Poisson's equation

[Mauro Sgroi]

I'm attempting to discretize the purely Neumann
problem for the Poisson's equation on a region V 

div(grad v)=f  on V 

(grad v)*n=g on S 

where S is the boundary of V and n the unit vector
normal to the surface S. 
The resulting matrix is singular and GetDP blow up
(with a NaN error). This is to be expected because of
not uniqueness of the solution to the weak problem
(the solution is known up to an addtiotional
constant). 
A unique solution to the system can be found by
imposing an additional condition on v such as
specifying v at one point or requiring that the
integral of v over V is equal to zero.
Is it possible to use one of the above strategies in
GetDP (the second would the better)?
I've tried to impose a Dirichlet boundary condition on
one node: this works only if the node is on the
boundary S but not if the node is on the computational
domain V.
In which way can I impose the second condition
defining a global quantity? Can you give me an
example?
Do you think that the Green's function approach would
be useful for my problem? If yes, in which way can I
use it in GetDP?

Thanks in advance and best regards,
Mauro Sgroi.
Italy.  


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