Abstract: Finite element methods (FEMs) on nonconforming meshes have been much studied in the literature. In all earlier works on such methods ,  some constraints must be imposed on the degrees of freedom on the edge/face  with hanging nodes  in order to maintain continuity, which make the numerical implementation more complicated. In this paper, we present two FEMs on quadrilateral nonconforming meshes which are constraint-free. Furthermore, we establish the corresponding residual-based a posteriori error estimation. We also  present extensive numerical testing results to systematically  compare the performance among three adaptive quadrilateral FEMs: the constraint-free adaptive Q1 FEM on quadrilateral nonconforming meshes with hanging nodes developed herein, the adaptive Q1 FEM based on quadrilateral red-green refinement  without any hanging node and the classical adaptive Q1  FEM  on quadrilateral nonconforming meshes  with constraints on hanging nodes.

Location: 606 Conference Room
Date and time: Nov 11, 2011   14:30