Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin methods, Numerical Methods for Partial Differential Equations
Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin methods, Numerical Methods for Partial Differential Equations
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一类弱伽辽金方法的超接近分析和多项式保全恢复，偏微分方程的数值方法
DOI：
10.1002/num.22201/full
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Z. Zhang
中科院分区：
文献类型：
--
作者：
R. Wang;R. Zhang;X. Zhang;Z. Zhang
本文分析了求解二阶椭圆问题的一类弱Galerkin（WG）有限元方法的收敛性和超逼近性。证明了WG解是超逼近于利用Lobatto点的拉格朗日插值。这种超接近性是通过一些新设计的稳定化项获得的。一个后处理技术，使用多项式保持恢复（PPR）介绍了WG近似。对PPR恢复的梯度进行了超收敛分析。数值例子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.