Abstract: For one-dimensional problems of Ritz Finite Element Method (FEM), an error estimate is presented for the simplified form of the Element Energy Projection (EEP) method used for super-convergence computation in post-processing stage of FEM. The mathematical analysis proves that for elements of degree (>1) with sufficiently smooth solutions, EEP solutions of the simplified form are capable of producing super-convergent solutions with convergence order of for both displacements and stresses at any point on an element, i.e. EEP simplified form obtains at least one order higher displacements and at least two order higher stresses than conventional FEM solutions.