Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements

Abstract

Abstract The superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4‐node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9‐node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4‐node quadrilaterals.