Re: [Getfem-users] Jump conditions on a surface.

[Yves Renard]

Dear Ronan,

You can use the level set strategy to describe S and define a finite element 
method which is discontinuous across this interface. But, there is in fact a 
little difficulty to compute the integral you need because on the surface 
itself, the value on the interface of the base function of the xfem (the 
mesh_fem_level_set object) is not guaranty. This is indeed a problem that we 
want to solve in a near future because we need to prescribe non elementary 
interface limit condition (such as contact condition or jump condition as you 
have).

If the interface is static and the mesh is conformal to this interface, there 
is a tool to partition a finite element method into two with regard to this 
interface. You can partition a fem into two or more parts with the method

mf_u.set_dof_partition(cv, i)

where cv is the element number and i is the zone number. Doing so, the dof 
between two zones will not be identified and you can represent a 
discontinuity between these two zones. In order to compute the integral you 
need, you have to define two mesh regions which will describe one side of the 
surface S and the other one respectively. Then you can integrate the terms 
you need with the usual strategy.

Yves.


Le mardi 15 mai 2007 09:16, vous avez écrit :
> Dear getfem experts,
>
> I would like to solve a (relatively simple) problem with jump conditions
> on an surface S.
>
> More precisely, if O denotes the domain, the variational form is the
> following :
> \int_O \sigma \grad u \grad v dx + \int_S \alpha [u][v] ds = <source terms>
> where [u] is the jump of u over S.
>
> Is there some elegant solution to implement this?
> If I have to use the level set strategy (NB: the surface is static and I
> can easily include it in the mesh), how can I translate the \int_S
> \alpha [u][v] ds integration?
>
> I will be glad to supply you further details.
> Thank you in advance for your answer,
> Best regards,
> Ronan Perrussel

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  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
  Pole de Mathematiques, INSA de Lyon          fax : (33) 04.72.43.85.29
  Institut Camille Jordan - CNRS UMR 5208
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard
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