xFEM numerical implementation
 

Hello,
I was wondering if someone could help me implement the xfem method in an incompressible multi-phase flow framework!

I'm currently having problems with the numerical integration part of the code. When evaluating the integral over the split element, the sum of the individual parts is not equivalent to that over the whole element! I'm using a simple function of:

int( N * dN/dx) dx dy

where (N) is the shape function, and (x,y) are the global element coordinates.
I don't quite understand how element splitting is done, and how it does not increase the number of degrees of freedom. Most papers I've seen indicate that the splitting is done for the sole purpose of integration.

I'm currently doing the following:
https://drive.google.com/file/d/0BxO...ew?usp=sharinghttps://drive.google.com/file/d/0BxO...ew?usp=sharinghttps://drive.google.com/file/d/0BxO...ew?usp=sharing

Any ideas/thoughts would be appreciated.
Thank you,
A. Bakkar