[Getdp] @D axisymmetric electrostatic problem

[Patrick Dular]

Nacho,

In your file, there is no particular treatment done on the 
axisymmetrical axis. I understand that you have fixed non-homogenous 
Neumann boundary conditions on some surfaces. Nevertheless, the 
homogeneous Neumann boundary condition on the axisymmetrical axis is 
implicit and does not need any explicit Galerkin term in the equations, 
which is the case in your formulation as well as in Gilles' one. The 
fact that you have added region 'SymAx' in the basis function support 
has no effect.

The problem with a Neumann (or natural) boundary condition is that it 
cannot be satisfied exactly, on any boundary of the studied domain. With 
an electric scalar potential formulation, this Neumann B.C. is relative 
to the normal derivative of the potential. In the same way, this normal 
derivative will be discontinuous at the interface between each pair of 
finite element. A way to improve the accuracy is to refine the mesh or 
to increase the finite element order.

Best regards,

Patrick

Nacho Andres wrote:

>Yes sure,
>Have a look to the pro file that I attached.
>Best Regards,
>Nacho
>
>On Wed, 2005-04-06 at 16:14, Patrick Dular wrote:
>  
>
>>Nacho,
>>
>>Could you send a example illustrating what you explain? Thank you.
>>
>>Patrick
>>    
>>