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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.