Zhang, Zhimin; Lin, Runchang Ultraconvergence of ZZ patch recovery at mesh symmetry points. (English) Zbl 1045.65096 Numer. Math. 95, No. 4, 781-801 (2003). The authors analyze mathematically the ultraconvergence property of the Zienkiewicz-Zhu (ZZ) gradient patch recovery techniques [cf. O. C. Zienkiewicz and J. Z. Zhu, Comput. Methods Appl. Mech. Eng. 101, No. 1–3, 207–224 (1992; Zbl 0779.73078)]. They use different smoothing strategies under the least-squares fitting for Q8 (eight-node serendipity element) and Q9 (nine-node tensor product element) finite elements. Some numerical tests are reported concerning the ultraconvergence property of the Q8 element. This is a nice and well written paper. Reviewer: Michel Bernadou (Paris La Defense) Cited in 12 Documents MSC: 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74S05 Finite element methods applied to problems in solid mechanics 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:Q8 eight-node serendipity element; Q9 nine-node tensor product element; ultraonvergence property; Zienkiewicz-Zhu gradient patch recovery technique; numerical examples; smoothing strategies; finite elements Citations:Zbl 0779.73078 PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{R. Lin}, Numer. Math. 95, No. 4, 781--801 (2003; Zbl 1045.65096) Full Text: DOI Link