Superconvergence of tricubic block finite elements (Q1041570)

The authors consider the boundary value problem \[ -\Delta u=f\quad\text{ in }\Omega ;\qquad u=0 \quad \text{ on } \partial \Omega, \] where \(\Omega \) is a rectangular domain in \(\mathbb R^{3}\). The approximate solution \(u_{h}\) of this problem can be obtained using the finite element method on a uniform mesh, but using an interpolation operator of \(u_{h}\) it is proved that the error estimate has the order \(0(h^{5})\). Some notations in this paper are not usual.