Supercloseness analysis and polynomial preserving Recovery for a class of weak Galerkin Methods
Supercloseness analysis and polynomial preserving Recovery for a class of weak Galerkin Methods
复制标题
一类弱伽辽金法的超接近分析与多项式保全恢复
DOI：
10.1002/num.22201
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发表时间：
2018
影响因子：
3.9
通讯作者：
Zhimin Zhang
中科院分区：
文献类型：
--
作者：
Ruishu Wang;Ran Zhang;Xu Zhang;Zhimin Zhang
本文分析了一类求解二阶椭圆型问题的弱Galerkin(WG)有限元方法的收敛和超封闭性质。利用Lobatto点证明了WG解与拉格朗日插值法是超接近的。这种超贴近行为是通过一些新设计的稳定化条件获得的。介绍了一种基于多项式保值恢复(PPR)的WG近似后处理技术。对PPR恢复的梯度进行了超收敛分析。文中给出了数值算例来说明我们的理论结果。
In this article, 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 interpolant using Lobatto points. This supercloseness behavior is obtained through some newly designed stabilization terms. A postprocessing technique using polynomial preserving recovery (PPR) is introduced for the WG approximation. Superconvergence analysis is performed for the PPR recovered gradient. Numerical examples are provided to illustrate our theoretical results.