  The eXtended Finite Element Method (XFEM) is used to solve interface problems
with an unfitted mesh. We present an implementation of the XFEM in the
FEM-library deal.II. The main parts of the implementation are (i) the
appropriate quadrature rule; (ii) the shape functions for the extended part of
the finite element formulation; (iii) the boundary and interface conditions. We
show how to handle the XFEM formulation providing a code that demonstrates the
solution of two exemplary interface problems for a strong and a weak
discontinuity respectively. In the weak discontinuity case, the loss of
conformity due to the blending effect and its remedy are discussed.
Furthermore, the optimal convergence of the presented unfitted method is
numerically verified.
