[Getdp] Surface integral.

[Ianenko, Evgueni]

Dear community,

I am sorry to put this question once more, but I have searched (and read)
all posts on surface integrals, and still have no idea how to solve this
simple problem in GetDP. I just can't beleive, that it is not possible
in such an impressively powerful package.

To formulate the question, I will use the simpliest 3D Laplace equation for electric
potential. I have Form0 function space for unknown potential U with Dirichlet
boundary conditions on some surfaces.

I want to calculate a charge on certain surfaces with Dirichlet BC, integrating
flux vector through these surfaces, something like:

Integral {[{Grad U}*Normal[]]; In DomainSurface; Jacobian JSur; Integration I1;}

or, at least:

Integral {[Norm[{Grad U}]]; In DomainSurface; Jacobian JSur; Integration I1;}

The problem here seems to be following: I need 3D flux vector {Grad U} from 3D domain,
and also 3D Normal[] vector, but from 2D domain (Normal[] is not defined on Tetrahedrons).
This scalar product has to be integrated again over 2D surface.

All my attempts to resolve this conflict failed - either I have to integrate
over volume to get correct {Grad U}, or I get {Grad U} in 2D domain, which is obviously zero.
This happens not only in post-processing, but also for integral quantities
in formulation, or even additional Form1 coefficients for desired surfaces.

On the other hand I can easily get correct values for:

E = Local {[{Grad U}]; In DomainVolume; Jacobian JVol; Integration I1;}

with post-operation:

Print [E, OnElementsOf DomainVolume, Skin];

I would appreciate any comments on how to resolve this issue.

Thank you in advance,
sincerely,

Evgeny Yanenko.
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