  As X-FEM approximation does not need meshing of the crack, the method has
garnered a lot of attention from industrial point of view. This thesis report
summarises some of the concepts involved in Nitsche approach for resolving
boundary conditions in embedded interfaces using XFEM. We consider here cases
in which the jump of a field across the interface is given, as well as cases in
which the primary field on the interface is given. We will first derive the
basics of Nitsche method and then discretize it with X-FEM using shifted basis
enrichment. We will then implement this on an open source platform, Code-Aster.
