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Nacho,<br>
<br>
A null Neumann boundary condition is always implicit in a finite
element formulation. The jacobian is something else which has no
influence on that.<br>
<br>
This means that any surface on which no Dirichlet B.C. is given and for
which no non-zero weak term is added in the formulation always
implicitly supports a null Neumann B.C.<br>
<br>
Patrick<br>
<br>
<br>
Nacho Andres wrote:<br>
<blockquote type="cite"
cite="mid1112808300.6590.3438.camel@dutlasc.lr.tudelft.nl">
<pre wrap="">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:
</pre>
<blockquote type="cite">
<pre wrap="">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
</pre>
</blockquote>
<pre wrap=""><!---->
</pre>
</blockquote>
<br>
<pre class="moz-signature" cols="72">--
Patrick Dular, Dr. Ir., Research associate, F.N.R.S.
Department of Electrical Engineering and Computer Science
Unit of Applied Electricity
University of Liege - Montefiore Institute - B28 - Parking P32
B-4000 Liege - Belgium - Tel. +32-4 3663710 - Fax +32-4 3662910
E-mail: <a class="moz-txt-link-abbreviated" href="mailto:Patrick.Dular@ulg.ac.be">Patrick.Dular@ulg.ac.be</a></pre>
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