Re: [Getfem-users] question about nitsche

[Yves Renard]

Dear Wen,

Yes, the term D_u G[v] is the directional derivative of  "G" in the direction "v". Of course it is simply G(v) if the problem to be solved is linear.

The term  (Hu-g).(Hv)/ \gamma  prescribe the condition itself, The term HG.Hv cancel the Neumann term in the corresponding direction in order to be consistent (without this term, the formulation is simply a non-consistent penalization of the Dirichlet condition). It is simply obtained by the integration by part when passing from the strong formulation of the problem to the weak one.
Finally, the term \theta(Hu-g)H D_u G[v] is added such that the formulation derive from a potential energy for \theta = 1 (and variational problems).

Yves.




On 13/10/2015 17:00, Wen Jiang wrote:

Hi Yves,

I am reading the document about the Nitsche's method for Dirichlet boundary conditions. (http://download.gna.org/getfem/html/homepage/userdoc/model_Nitsche.html)

I do not quite understand the weak form in the "Generic Nitsche's method for a Dirichlet condition" section. Could you explain the third term HG \dot Hv and the last term HD_u G[v]? Does the D_u mean the derivative of G[v]? 

Thanks,

Wen

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  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
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