Exact smooth piecewise polynomial sequences on Alfeld splits
Numerical Analysis
2018-07-17 v1
Abstract
We develop exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vertices of an -simplex with its barycenter. We show that, on these triangulations, the kernel of the exterior derivative has enhanced smoothness. Byproducts of this theory include characterizations of discrete divergence-free subspaces for the Stokes problem, commutative projections, and simple formulas for the dimensions of smooth polynomial spaces.
Cite
@article{arxiv.1807.05883,
title = {Exact smooth piecewise polynomial sequences on Alfeld splits},
author = {Guosheng Fu and Johnny Guzman and Michael Neilan},
journal= {arXiv preprint arXiv:1807.05883},
year = {2018}
}