# [Getdp] Neumann boundary condition

Tammo.Heeren at AlconLabs.com Tammo.Heeren at AlconLabs.com
Fri Mar 21 01:10:23 CET 2008

Hi Luis,

Thank you for your response and the code. I am working my way through it
to understand it.
Here is what I understand so far, please correct me if I am wrong.

---
1. Galerkin { [ Dof{d u} , {d u} ] ; In OMEGA ; Jacobian Vol ;
Integration Int ; }
2. Galerkin { [ -f[] , {u} ] ; In OMEGA ; Jacobian Vol ; Integration Int
; }
3. Galerkin { [ -g[] , {u} ] ; In GAMMA ; Jacobian Sur ; Integration Int
; }
4. Galerkin { [ Dof{u} , {uo} ] ; In OMEGA ; Jacobian Vol ; Integration
Int ; }
5. Galerkin { [ Dof{uo} , {uo} ] ; In OMEGA ; Jacobian Vol ; Integration
Int ; }
---

- GAMMA is a line surrounding surface OMEGA. Both are in domain DOMAIN.
- I assume that GAMMA and OMEGA share nodes
- div( grad(u) ) - f = 0 in OMEGA
- f is defined in DOMAIN, though I suppose you only have to define it in
OMEGA
- u is defined in DOMAIN as a Form0 FunctionSpace
- grad(u) comes for the Form0 FunctionSpace and the {d u} in the second
part of the Galerkin
- div(...) stems from the {d u} in the first part of the Galerkin
- the -f comes from the second Galerkin term

I don't understand where
> \frac{\partial u}{\partial n} = g in \Gamma
comes from.

- if GAMMA and OMEGA share nodes, than the Galerkin terms 1 and 2 are
also valid in GAMMA
- then have div( grad(u) ) - f - g = 0 in GAMMA

I am also a little fuzzy about Galerkin terms 4 and 5.
- I assume that Galerkin 4. simply copies the function space u onto uo
- u is defined as Form0 and uo is defined as Scalar (where is the
difference?)
- does Galerkin 5. then simply copy uo onto itself?

If anybody else can contribute some inside, I would be happy to hear it.

Gruesse,

Tammo

---
FunctionSpace {
{ Name FSU ; Type Form0 ;
BasisFunction {
{ Name sn ; NameOfCoef un ; Function BF_Node ;
Support DOMAIN ; Entity NodesOf[ All ] ; }
}
Constraint {
}
}
{ Name FSU0 ; Type Scalar ;
BasisFunction {
{ Name so ; NameOfCoef uo ; Function BF_Region ;
Support OMEGA ; Entity OMEGA ; }
}
Constraint {
}
}
}

Formulation {
{ Name Uform ; Type FemEquation ;
Quantity {
{ Name u; Type Local;  NameOfSpace FSU; }
{ Name uo; Type Local;  NameOfSpace FSU0; }
}
Equation {
// div( grad( u ) ) = f in Omega (Surface)
Galerkin { [ Dof{d u} , {d u} ] ; In OMEGA ; Jacobian
Vol ; Integration Int ; }
Galerkin { [ -f[] , {u} ] ; In OMEGA ; Jacobian Vol ;
Integration Int ; }
Galerkin { [ -g[] , {u} ] ; In GAMMA ; Jacobian Sur ;
Integration Int ; }
Galerkin { [ Dof{u} , {uo} ] ; In OMEGA ; Jacobian Vol ;
Integration Int ; }
Galerkin { [ Dof{uo} , {uo} ] ; In OMEGA ; Jacobian Vol
; Integration Int ; }
}
}
}
---

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