Gradient recovery for elliptic interface problem: II. Immersed finite element methods
Gradient recovery for elliptic interface problem: II. Immersed finite element methods
复制标题
DOI：
10.1016/j.jcp.2017.03.003
复制
发表时间：
2016-07
期刊：
影响因子：
--
通讯作者：
Hailong Guo;Xu Yang
中科院分区：
文献类型：
--
作者：
Hailong Guo;Xu Yang
本文是第二篇关于椭圆界面问题梯度恢复的研究。在我们之前的工作中，Guo和Yang（2016）[17]，我们开发了一种基于贴体网格的有限元方法的新型梯度恢复技术。本文提出了两种浸入界面有限元方法的新梯度恢复方法：对称一致浸入有限元方法（Ji et al.（2014）[23]）和Petrov-Galerkin浸入有限元方法（Hou et al.（2004）[22]，Hou and Liu（2005）[20]）。与基于贴体网格的梯度恢复方法相比，新方法提供了一种在规则网格上恢复梯度的统一方法。数值例子证实了这两种梯度恢复方法的超收敛性。此外，他们提供了渐近精确posteriorerror估计浸入有限元方法。
This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work Guo and Yang (2016) [17], we developed a novel gradient recovery technique for finite element method based on the body-fitted mesh. In this paper, we propose new gradient recovery methods for two immersed interface finite element methods: symmetric and consistent immersed finite method (Ji et al. (2014) [23]) and Petrov–Galerkin immersed finite element method (Hou et al. (2004) [22], and Hou and Liu (2005) [20]). Compared to the body-fitted mesh based gradient recovery method, the new methods provide a uniform way of recovering gradient on regular meshes. Numerical examples are presented to confirm the superconvergence of both gradient recovery methods. Moreover, they provide asymptotically exacta posteriorierror estimators for both immersed finite element methods.