Superconvergence of tetrahedral linear finite elements

In this paper, we show that the piecewise linear finite element solution uh and the linear interpolation uI have superclose gradient for tetrahedral meshes, where most elements are obtained by dividing approximate parallelepiped into six tetrahedra. We then analyze a post-processing gradient recovery scheme, showing that the global L2 projection of ∇uh is a superconvergent gradient approximation to ∇u.