TY - JOUR
T1 - Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis
AU - Xuying Zhao, Shipeng Mao & Zhong-Ci Shi
JO - Journal of Computational Mathematics
VL - 5
SP - 621
EP - 644
PY - 2010
DA - 2010/10
SN - 28
DO - http://doi.org/10.4208/jcm.1001-m3006
UR - https://global-sci.org/intro/article_detail/jcm/8541.html
KW - Finite element method, Adaptive algorithm, Hanging node, 1-irregular mesh,
Convergence analysis.
AB - <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>