The superconvergence patch recovery technique and data transfer operators in 3D plasticity problems

A decade has passed since the first appearance of the superconvergent patch recovery (SPR) method introduced by Zienkiewicz and Zhu [The superconvergence patch recovery and a posteriori error estimates, part I: the recovery techniques, Int. J. Numer. Methods Eng. 33 (1992) 1331–1364; The superconvergence patch recovery and a posteriori error estimates, part II: error estimates and adaptivity, Int. J. Numer. Methods Eng. 33 (1992) 1365–1380; Superconvergence and the superconvergent patch recovery, Finite Elem. Anal. Des. 19 (1995) 11–23]. The method is now widely used in engineering practices for its robustness and efficiency in computer implementation. This paper presents an extension of the SPR technique to 3D nonlinear problems with its application to 3D data transferring of continuum nonlinear mechanics. The transfer operators are presented for mapping of the state and internal variables between different meshes. Aspects of the transfer operators are presented in 3D superconvergent path recovery technique based on C0C0, C1C1 and C2C2 continuity using tetrahedral elements. Finally, the efficiency of the proposed model and computational algorithms is demonstrated by several numerical examples.