A New Finite Element Gradient Recovery Method: Superconvergence Property
A New Finite Element Gradient Recovery Method: Superconvergence Property
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DOI：
10.1137/s1064827503402837
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发表时间：
2005-04
期刊：
影响因子：
--
通讯作者：
Zhimin Zhang;Ahmed Naga
中科院分区：
文献类型：
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作者：
Zhimin Zhang;Ahmed Naga
这是一系列论文中的第一篇，其中介绍和分析了一种新的梯度恢复方法。证明了该方法对任意阶平移不变有限元空间是超收敛的。该方法保持了Zienkiewicz-Zhu补丁恢复方法的简单性、高效性和超收敛性。此外，对于均匀三角形网格，该方法在人字形模式下对线性元是超收敛的，而在规则模式下对二次元在单元边缘中心处是超收敛的。这种新的梯度恢复技术的应用将在即将发表的论文中讨论。
This is the first in a series of papers in which a new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz--Zhu patch recovery method. In addition, for uniform triangular meshes, the method is superconvergent for the linear element under the chevron pattern, and ultraconvergent at element edge centers for the quadratic element under the regular pattern. Applications of this new gradient recovery technique will be discussed in forthcoming papers.