Adaptive quadrilateral and hexahedral finite element methods with hanging nodes and convergence analysis

Abstract

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 ℚm elements which covers both the two- and three-dimensional cases in a unified fashion. Copyright 2010 by AMSS, Chinese Academy of Sciences.