Abstract: For an variable coefficients elliptic equation in 3D,weak estimates for the block finite element over rectangular parallelepiped partitions of the domain are obtained by using three- dimensional interpolation operator of projection type and interpolating approximation properties.Furthermore,in combination with three-dimensional discrete Green functions,the author derives the maximum-norm superapproximation results with high accuracy of the displacement and gradient for block finite elements.

Key words: variable coefficients elliptic equation, block finite element, interpolation operator of projection type, discrete Green funtions, superapproximation