Adaptive finite element methods in computational mechanics
Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
Error indicators and adaptive remeshing in large deformation finite element analysis
Finite Elements in Analysis and Design
Superconvergence and the superconvergent patch recovery
Finite Elements in Analysis and Design - Special issue: Robert J. Melosh Medal Competition
Conservative remapping and region overlays by intersecting arbitrary polyhedra
Journal of Computational Physics
Ultraconvergence of the patch recovery technique II
Mathematics of Computation
Mixed Finite Element Methods on Nonmatching Multiblock Grids
SIAM Journal on Numerical Analysis
A modified superconvergent patch recovery method and its application to large deformation problems
Finite Elements in Analysis and Design
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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 C"0, C"1 and C"2 continuity using tetrahedral elements. Finally, the efficiency of the proposed model and computational algorithms is demonstrated by several numerical examples.