Abstract：The fundamental difference between the finite element method(FEM) and the meshless method(MM) lies in the difference of the construction methods of the shape function. But the two kinds of shape functions both serve as a partition of unity. Integration of the weak form over the problem domain is needed when solving the partial differential equation using the Galerkin method. The newly presented quadrature method based on partition of unit provides a unified approach for the integration of the weak form in FEM and MM. MM is advantageous over the traditional FEM in the problems involved with the propagation of crack and large mesh deformation and so on. But the imposition of essential boundary condition and the treatment of discontinuous field variable and the derivative are somewhat troublesome，and the computation cost is large. The natural element method(NEM) is a newly appeared numerical method to solve the PDE. NEM assumes the characteristics of MM and the advantages of finite element method，so it is a most promising method.
