Superconvergence of tricubic block finite elements

In this paper, we first introduce interpolation operator of projection type in three dimensions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W ^{2, 1}-seminorm of the discrete derivative Green’s function and the weak estimates, we show that the tricubic block finite element solution u _h and the tricubic interpolant of projection type Π _h ³ u have superclose gradient in the pointwise sense of the L ^∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived. This work was supported by Natural Science Foundation of Ningbo City (Grant No. 2008A610020), National Natural Science Foundation of China (Grant No. 10671065) and the Scientific Research Fund of Hunan Provincial Education Department (Grant Nos. 07C576, 03C212)