Linear dependence problems of partition of unity-based generalized FEMs

A known problem of partition of unity-based generalized finite element methods (referred to as GFEM) is the linear dependence problem, which leads to singular global (stiffness) matrices. Thus far attempts to eliminate the linear dependence problem have been unsuccessful. Numerical experiments are carried out among several GFEMs to investigate the problem. Based on the numerical experiments, simple but effective approaches to eliminating the linear dependence problem are suggested.