Local gradient and stress recovery for triangular elements

A macroelement post-processing technique is proposed to recover higher order gradients and stresses in two-dimensional elasticity based on the least-square residuals of the equilibrium equation, irrotationality condition and kinematic relation evaluated at certain superconvergent points. Stability and convergence are established and a priori rates of convergence are proved for stable macroelement configurations. Numerical experiments confirming the predicted rates are presented. We also propose an error indicator defined by a natural norm associated with the macroelement post-processing technique.