@Article{CiCP-14-621,
author = {Jianguo Xin, Wei Cai and Nailong Guo},
title = {On the Construction of Well-Conditioned Hierarchical Bases for $\mathcal{H}(div)$-Conforming $\mathbb{R}^n$ Simplicial Elements},
journal = {Communications in Computational Physics},
year = {2013},
volume = {14},
number = {3},
pages = {621--638},
abstract = {<p style="text-align: justify;">Hierarchical bases of arbitrary order for &nbsp;$\mathcal{H}(div)$-conforming triangular and
tetrahedral elements are constructed with the goal of improving the conditioning of the
mass and stiffness matrices. For the basis with the triangular element, it is found numerically that the conditioning is acceptable up to the approximation of order four, and
is better than a corresponding basis in the dissertation by Sabine Zaglmayr [High Order Finite Element Methods for Electromagnetic Field Computation, Johannes Kepler
Universität, Linz, 2006]. The sparsity of the mass matrices from the newly constructed
basis and from the one by Zaglmayr is similar for approximations up to order four.
The stiffness matrix with the new basis is much sparser than that with the basis by
Zaglmayr for approximations up to order four. For the tetrahedral element, it is identified numerically that the conditioning is acceptable only up to the approximation of
order three. Compared with the newly constructed basis for the triangular element,
the sparsity of the mass matrices from the basis for the tetrahedral element is relatively
sparser.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.100412.041112a},
url = {http://global-sci.org/intro/article_detail/cicp/7175.html}
}