Two issues of the XFEM method are adressed. The first one is the clip to vertex algorithm when a node is too close to the iso zero of the levelset that requires the definition of a treshold. The second one is the numerical integration in high order elements cut by the levelset. A solution to these two problems is presented.
Bricteux, G. (2008). Discontinuous fields integration in a structured mesh using the level set method. 8th. World Congress on Computational Mechanics, Venice. https://hdl.handle.net/2078.5/206122