Superconvergence Phenomena on Three-Dimensional Meshes
Keywords:
linear and quadratic tetrahedral elements, acute partitions, Poisson equation, postprocessing, supercloseness, averaging and smoothing operators, regular polytopes, combinatorial topology.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.