Abstract：Valid estimation of the posterior error is the first step to the implementation of adaptive analysis with the natural element method(NEM). For the successful applications of Z-Z error estimation in the adaptive finite element analysis and the element-free Galerkin method and its simplicity and high efficiency，the implementation of Z-Z method in NEM is attempted. When the NEM is used to solve the solid mechanics problems employing the displacement model，the strain and stress on the scattered nodes cannot be directly acquired form the displacement field because the derivatives on the nodes of the shape function do not exist. What is more，the linear interpolation property of the shape function between the adjacent boundary nodes results shows that the stress/strain is piecewise constant on the boundary. So recovery scheme is performed to extract strain/stress on the nodes and construct a smooth strain/stress field. Moving least squares method is used to extract strain/stress on the nodes from the displacement field acquired from the NEM solution. Then a smoothing stress/strain field can be attained through natural neighbor interpolation employing the recovered strain or stress on the nodes. Numerical examples show that the recovery scheme is feasible；both the accuracy and the convergence of the smoothing stress field are higher. Then difference of original stress field and the recovered stress field is calculated as the error estimation based on the Z-Z method. Numerical example shows that the Z-Z error estimator is feasible，simple and efficient.
