A3

Long Chen. Superconvergence of tetrahedral linear finite elements. International Journal of Numerical Analysis and Modeling, 3:273--282, 2006.

Chen.L2006.pdf

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 $\nabla u$.