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

Authors

  • Hao Pan Department of Applied Mathematics, Shandong Agricultural University, Taian, 271018, China
  • Zhimin Zhang Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal University, Changsha 410081, China
  • Lewei Zhao Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

Keywords:

Finite element method, post-processing, gradient recovery, superconvergence.

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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Published

2020-05-20

Issue

Vol. 17 No. 3 (2020)

Section

Articles