Reformulation of XFEM based on PUFEM for solving problem caused by blending elements

A lack of numerical accuracy in the standard extended finite element method (XFEM) is caused by ‘blending elements’, whose nodes are partially enriched. ‘The corrected XFEM’ proposed by Fries showed the effective improvement of this problem with a lot of numerical results. The theoretical approach of this proposal was however not sufficiently described. In the present paper, an approximation of the XFEM is reformulated based on the concept of the partition of unity finite element method (PUFEM) approximation, which assures the numerical accuracy in the entire domain, for solving the problem of blending elements. The form of the reformulated XFEM results in the coincidence with that of the corrected XFEM. It is therefore found out that the theoretical validation of the corrected XFEM is based on the PUFEM approximation. It is also found out that the problem of the blending elements in the application to two dimensional linear fracture mechanics has been sufficiently solved for actual use by the XFEM based on the PUFEM.