High accuracy analysis of tensor-product linear pentahedral finite elements for variable coefficient elliptic equations

For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W ^{1, 1}-seminorm of the discrete derivative Green’s function is given. Finally, the authors show that the derivatives of the finite element solution u _h and the corresponding interpolant Πu are superclose in the pointwise sense of the L ^∞-norm.