TY - JOUR T1 - Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis 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 -

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 $Q_m$ elements which covers both the two- and three-dimensional cases in a unified fashion.