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

• Published in: Computer methods in applied mechanics and engineering 1998-03, Vol.155 (1), p.15-30
• Main Authors: Tessler, Alexander, Riggs, H.Ronald, Freese, Colin E., Cook, Geoffrey M.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(97)00135-7

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.