@Article{JCM-39-333,
author = {Hu , Kaibo and Winther , Ragnar},
title = {Well-Conditioned Frames for High Order Finite Element Methods},
journal = {Journal of Computational Mathematics},
year = {2021},
volume = {39},
number = {3},
pages = {333--357},
abstract = {<p style="text-align: justify;">The purpose of this paper is to discuss representations of high order $C^0$ finite element
spaces on simplicial meshes in any dimension. When computing with high order piecewise
polynomials the conditioning of the basis is likely to be important. The main result of this
paper is a construction of representations by frames such that the associated $L^2$ condition
number is bounded independently of the polynomial degree. To our knowledge, such a representation has not been presented earlier. The main tools we will use for the construction
is the bubble transform, introduced previously in [1], and properties of Jacobi polynomials
on simplexes in higher dimensions. We also include a brief discussion of preconditioned
iterative methods for the finite element systems in the setting of representations by frames.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2001-m2018-0078},
url = {http://global-sci.org/intro/article_detail/jcm/18747.html}
}