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Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. (English) Zbl 0789.73064
Summary: The superconvergent patch derivative recovery method of O. C. Zienkiewicz and J. Z. Zhu [Int. J. Numer. Methods. Eng. 24, 337- 357 (1987; Zbl 0602.73063)] 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.

74S05Finite element methods in solid mechanics
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
74K20Plates (solid mechanics)