Pointwise supercloseness of the displacement for tensor-product quadratic pentahedral finite elements

In this work, we derive a weak estimate of the second type for tensor-product quadratic pentahedral finite elements over uniform partitions of the domain for the Poisson equation. Combining with an estimate for the W2,1-seminorm of the discrete Green's function, pointwise supercloseness of the displacement between the finite element approximation and the interpolant to the true solution is given.