(untitled) (Journal of Computational Mathematics, 2019)
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.