Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements

TLDR: In this article, 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.

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.