Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin method
Numerical Analysis
2019-10-18 v2
Abstract
In this paper, we analyze convergence and supercloseness properties of a class of weak Galerkin (WG) finite element methods for solving second-order elliptic problems. It is shown that the WG solution is superclose to the Lagrange type interpolation using Lobatto points. This supercloseness behavior is obtained through some newly designed stabilization terms. A post-processing technique using the polynomial preserving recovery (PPR) is introduced for WG approximation. Superconvergence analysis is carried out for the PPR approximation. Numerical examples are provided to verify our theoretical results.
Keywords
Cite
@article{arxiv.1610.05626,
title = {Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin method},
author = {Ruishu Wang and Ran Zhang and Xu Zhang and Zhimin Zhang},
journal= {arXiv preprint arXiv:1610.05626},
year = {2019}
}