An efficient method for computing local quantities of interest in elasticity based on finite element error estimation

Abstract

We present an efficient finite element method for computing the engineering quantities of interest that are linear functionals of displacement in elasticity based on a posteriori error estimate. The accuracy of quantities is greatly improved by adding the approximate cross inner product of errors in the primal and dual problems, which is calculated with an inexpensive gradient recovery type error estimate, to the quantities obtained from the finite element solution. With less CPU time, the accuracy of the improved quantities obtained with the proposed method on the coarse finite element mesh is similar to that of the quantities obtained from the finite element solutions on the finer mesh. Three quantities related to the local displacement, local stress and stress intensity factor are computed with the proposed method to verify its efficiency.