This paper presents two efficient integration schemes for the element-free Galerkin (EFG) method. They are able to let EFG with quadratic basis pass the quadratic patch test exactly in a numerical sense. The proposed two schemes, respectively, use three and one quadrature points in each background triangle cell and the derivatives of the nodal shape functions at these quadrature points are corrected by the introduced discrete divergence consistency (DDC) condition. Numerical results of benchmark examples demonstrate the improved accuracy, convergence, efficiency and stability by the proposed schemes.
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