Some New Developments of Polynomial Preserving Recovery on Hexagon and Chevron Patches

Some New Developments of Polynomial Preserving Recovery on Hexagon and Chevron Patches

Year:    2020

Author:    Hao Pan, Zhimin Zhang, Lewei Zhao

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2020-IJNAM-16865

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 3 : pp. 390–403

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Finite element method post-processing gradient recovery superconvergence.

Author Details

Hao Pan

Zhimin Zhang

Lewei Zhao