Article,
The Post-Processing Approach in the Finite Element Method—Part 1: Calculation of Displacements, Stresses and other Higher Derivatives of the Displacements
International Journal for Numerical Methods in Engineering, 20 (6): 1085--1109 (June 1984)
DOI: 10.1002/nme.1620200610
Abstract
This is the first in a series of three papers in which we discuss a method for 'post‐processing' a finite element solution to obtain high accuracy approximations for displacements, stresses, stress intensity factors, etc. Rather than take the values of these quantities 'directly' from the finite element solution, we evaluate certain weighted averages of the solution over the entire region. These yield approximations are of the same order of accuracy as the strain energy. We obtain error estimates, and also present some numerical examples to illustrate the practical effectiveness of the technique. In the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation.
