Superconvergence of Tetrahedral Linear Finite Elements

Abstract

In this paper, we show that the piecewise linear finite element solution $u_h$ and the linear interpolation $u_I$ 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 $L^2$ projection of $\nabla u_h$ is a superconvergent gradient approximation to $\nabla u$.