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Ultraconvergence of ZZ patch recovery at mesh symmetry points. (English) Zbl 1045.65096

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.

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

Citations:

Zbl 0779.73078
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