[Getdp] @D axisymmetric electrostatic problem

[Nacho Andres]

Dear Patrick,
I actually understood from my communications with Cristophe that the
null Neumann conditions at the symmetry axis were not implicit if I did
not include the latter into the Basis Function support. By including it,
getDP would try to approximate the Neumann condition at it, so including
those surfaces into the support of the basis functions would case the
iteration that the program does to make variations on those points in
some way, but not on those at which no Neumann and only Dirichlet
conditions exist, am I right? 
What you are suggesting is that the fact of using the JSurAxi jacobian
already does that already, is that so?

Nacho

Ps: As a matter of fact what I tried the first times was a) refining the
mesh and b) increasing the order of the basic functions. Good guess
then! ;D

On Wed, 2005-04-06 at 18:53, Patrick Dular wrote:
> 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