Overview and comparison of different variants of the XFEM

Different variants of the eXtended Finite Element Method (XFEM) have developed over the last years: The original, shifted, corrected, stable, and intrinsic XFEM. Herein, these variants are compared in terms of convergence rates and conditioning of the resulting systems of equations. Optimal convergence rates are achieved by the corrected, stable, and intrinsic XFEM for general enrichments. The original and shifted XFEM achieve optimal rates for selected enrichments only. In terms of the conditioning, it is found that the stable XFEM can be “optimal” in the sense that the same dependency on the mesh size as for the classical FEM is maintained. However, this finding only holds if one enrichment term is involved. In the presence of several enrichment terms, only the intrinsic XFEM yields well-conditioned systems of equations