@Article{IJNAM-17-3,
author = {Pan, Hao and Zhimin, Zhang and Zhao, Lewei},
title = {Some New Developments of Polynomial Preserving Recovery on Hexagon and Chevron Patches},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2020},
volume = {17},
number = {3},
pages = {390--403},
abstract = {<p style="text-align: justify;">Polynomial Preserving Recovery (PPR) is a popular post-processing technique for
finite element methods. In this article, we propose and analyze an effective linear element PPR
on the equilateral triangular mesh. With the help of the discrete Green&#39;s function, we prove
that, when using PPR to the linear element on a specially designed hexagon patch, the recovered
gradient can reach $O$($h$<sup>4</sup>| ln $h$|<sup>$\frac{1}{2}$</sup>) superconvergence rate for the two dimensional Poisson equation.
In addition, we apply PPR to the quadratic element on uniform triangulation of the Chevron
pattern with an application to the wave equation, which further verifies the superconvergence
theory.</p>},
issn = {2617-8710},
doi = {https://doi.org/2020-IJNAM-16865},
url = {https://global-sci.com/article/83025/some-new-developments-of-polynomial-preserving-recovery-on-hexagon-and-chevron-patches}
}