Superconvergence Phenomena on Three-Dimensional Meshes

Abstract

We give an overview of superconvergence phenomena in the finite element method for solving three-dimensional problems, in particular, for elliptic boundary value problems of second order over uniform meshes. Some difficulties with superconvergence on tetrahedral meshes are presented as well. For a given positive integer $m$ we prove that there is no tetrahedralization of $R^3$ whose all edges are $m$-valent.