Volume 17, Issue 3
Some New Developments of Polynomial Preserving Recovery on Hexagon and Chevron Patches

Int. J. Numer. Anal. Mod., 17 (2020), pp. 390-403.

Published online: 2020-05

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• Abstract

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'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$4| ln $h$|$\frac{1}{2}$) 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.

65N30, 65N80

pan_hao2003@163.com (Hao Pan)

zzhang@math.wayne.edu (Zhimin Zhang)

zhao.lewei@wayne.edu (Lewei Zhao)

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@Article{IJNAM-17-390, author = {Pan , HaoZhang , Zhimin 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 = {

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'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$4| ln $h$|$\frac{1}{2}$) 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/16865.html} }
TY - JOUR T1 - Some New Developments of Polynomial Preserving Recovery on Hexagon and Chevron Patches AU - Pan , Hao AU - Zhang , Zhimin AU - Zhao , Lewei JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 390 EP - 403 PY - 2020 DA - 2020/05 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/16865.html KW - Finite element method, post-processing, gradient recovery, superconvergence. AB -

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'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$4| ln $h$|$\frac{1}{2}$) 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.

Hao Pan , Zhimin Zhang & Lewei Zhao . (2020). Some New Developments of Polynomial Preserving Recovery on Hexagon and Chevron Patches. International Journal of Numerical Analysis and Modeling. 17 (3). 390-403. doi:
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