REVISITING THE LOSS AND RECOVERY OF DISPLACEMENT ACCURACY IN FEM AS SEEN FROM MATRIX DISPLACEMENT METHOD ¹⁾

This paper is a revisit of Ref.1, where it is shown that the errors from one-dimensional finite element (FE) results mostly come from the element fixed-end solutions. Based on this concept, the element energy projection (EEP) method for the super-convergence calculation is developed. Moreover, when the EEP technique is applied to the adaptive FE analysis to estimate and control the errors in FE solutions, the solutions satisfying the user pre-set error tolerances in the maximum norm can be obtained. Recent introspection leads to a realization that the essence in Ref.1 has not been fully exploited: since the element fixed-end solutions are the major source of errors, then it is possible to calculate the errors a priori by using the EEP method, immediately generating a desirable mesh without the need for the FE analysis in advance. This paper gives a brief introduction to this novel idea and some initial numerical results are given to show the validity and effectiveness of the proposed technique.