Abstract: Recently, based on mechanics principle, Yuan’s group proposed a one-dimensional finite element superconvergent postprocessing scheme-Element-Energy-Projection (EEP) method. A large number of numerical examples show that, provided that the exact solution is sufficiently smooth, the EEP method nodal recovery stress have the accuracy of O(h2m) for elements with m degrees-of-freedom. Using a fundamental estimation formula, the linear element nodal recovery stress is firstly proved to have the accuracy of O(h2) by the EEP method. Secondly, a simplification of EEP method for the calculation of higher order element’s interior point is pointed out.