CFD Online Discussion Forums

CFD Online Discussion Forums (http://www.cfd-online.com/Forums/)
-   Main CFD Forum (http://www.cfd-online.com/Forums/main/)
-   -   Neumann Boundary Condition in FEM (http://www.cfd-online.com/Forums/main/117196-neumann-boundary-condition-fem.html)

kingmaker May 4, 2013 06:39

Neumann Boundary Condition in FEM
 
Hello
I am trying to implement a small FEM code for solving Poisson equation on arbitrary domains. I understand how to implement Drichlet Boundary conditions after formulating the Global stiffness matrix.

But I do not quite understand how to implement Neumann Boundary conditions. For example I have to integrate over the the boundary of the element. But what if a particular element does not have a boundary, like its completely in the interior.

Also when we integrate over the boundary what should be done when a element has only one of its nodes on the boundary ?

Thanks in advance

Rami May 29, 2013 04:21

Hi Aditya,

The Poisson equation u,ii=f FEM formulation is derived using the usual Galerkin shape-function-weighted integration and the Gauss divergence theorem. You get the element boundary term as the surface integral over the element of (NI du/dn), where NI is the shape function of node I and du/dn is the derivative of u in the the outward-normal direction to the face.

When the element is internal, the same face is shared by two elements, so this term cancels in the assembly. This is also true if a single node of it is on the boundary, but the face is internal.

For en external face, Neumann BC means the du/dn is prescribed, so the integral is readily calculated. In the special case du/dn=0 (no flux), this term is 0.

I hope this helps,
Rami


All times are GMT -4. The time now is 13:24.