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A GFEM without extra dof is developed. Without the extra dof, the resulting linear system becomes independent—in size—of the order of local approximation, the resulting PU approximation becomes free of linear dependence, and the resulting stiffness matrix becomes good conditioned. Numerical studies show the new GFEM’s excellent convergence properties and excellent stability.
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...
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