A SCHEME WITH OPTIMAL ORDER OF SUPER-CONVERGENCE BASED ON EEP METHOD: III MATHEMATICAL PROOF
Based on the Element Energy Projection (EEP) method, an improved scheme with optimal order of super-convergence, is presented for one-dimensional C 0 FEM, i.e., FEM sulotions can be obtained through the scheme for the elements with sufficient smooth property and m degrees. The proposed scheme is capable of producing O ( h 2m) super-convergence for both displacements and stresses at any point on an element in post- processing stage. The entire work is composed of three parts, i.e. formulation, numerical results as well as mathematical analysis. The present paper is the third in the series and gives the mathematical proof of the optimal O ( h 2m)super-convergence for the proposed scheme.