An improved variational method for finite element stress recovery and a posteriori error estimation

Abstract

A new variational formulation is presented which serves as a foundation for an improved finite element stress recovery and a posteriori error estimation. In the case of stress predictions, interelement discontinuous stress fields from finite element solutions are transformed into a C 1-continuous stress field with C 0-continuous stress gradients. These enhanced results are ideally suited for error estimation since the stress gradients can be used to assess equilibrium satisfaction. The approach is employed as a post-processing step in finite element analysis. The variational statement used herein combines discrete-least squares, penalty-constraint, and curvature-control functionals, thus enabling automated recovery of smooth stresses and stress gradients. The paper describes the mathematical foundation of the method and presents numerical examples including stress recovery in two-dimensional structures and built-up aircraft components, and error estimation for adaptive mesh refinement procedures.