Pointwise supercloseness of tensor‐product block finite elements

In this article, we first introduce interpolation operator of projection type in three dimensions, from which we then derive weak estimates for tensor‐product block finite elements of degree m ≥ 1. Finally, using estimates for the discrete Green's function and the discrete derivative Green's function, we prove that both of the gradient and the function value of the finite element solution u h and the corresponding interpolant Π m u of projection type and degree m are superclose in the pointwise sense of the L ∞ ‐norm. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009