CALCULATION OF ERRORS OF NODAL DISPLACEMENTS IN ONE-DIMENSIONAL FINITE ELEMENT METHODS USING ELEMENT ENERGY PROJECTION TECHNIQUE

Using super-convergent solutions calculated by the Element Energy Projection (EEP) method, equivalent nodal load vectors from the residual load term were derived in this paper without changing the finite element (FE) meshes and the global stiffness matrices. The subsequent back-substitutions can generate highly accurate estimates for the errors of nodal displacements and hence greatly improve the nodal accuracy. Taking a general second-order ordinary differential equation as the model problem, the algorithm of the proposed method and associated numerical examples were given to show that the proposed method is simple and effective, and that using elements of degree m≥1, the improved nodal displacements can gain the super-super-convergence orders h^2m+2 and h^{3m+mod(m, 2)} for simplified and condensed EEP forms, respectively. A variety of significant further extensions and applications were also discussed.