TY - JOUR
T1 - Superconvergence Phenomena on Three-Dimensional Meshes
AU - Křížek , Michal
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 43
EP - 56
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/919.html
KW - linear and quadratic tetrahedral elements, acute partitions, Poisson equation, postprocessing, supercloseness, averaging and smoothing operators, regular polytopes, combinatorial topology.
AB - <p style="text-align: justify;">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.</p>