@Article{JCM-28-621,
author = {Xuying Zhao, Shipeng Mao and Zhong-Ci Shi},
title = {Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis},
journal = {Journal of Computational Mathematics},
year = {2010},
volume = {28},
number = {5},
pages = {621--644},
abstract = {<p style="text-align: justify;">In this paper we study the convergence of adaptive finite element methods for the general non-affine equivalent quadrilateral and hexahedral elements on 1-irregular meshes with hanging nodes. Based on several basic ingredients, such as quasi-orthogonality, estimator reduction and Döfler marking strategy, convergence of the adaptive finite element methods for the general second-order elliptic partial equations is proved. Our analysis is effective for all conforming&nbsp;$Q_m$ elements which covers both the two- and three-dimensional cases in a unified fashion.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1001-m3006},
url = {http://global-sci.org/intro/article_detail/jcm/8541.html}
}