Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements

This paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods. The theory assures reliability and efficiency of explicit residual error estimates up to data oscillations under the conditions (H1)-(H2) and applies to several nonconforming finite elements: the Crouzeix-Raviart triangle element, the Han parallelogram element, the nonconforming rotated (NR) parallelogram element of Rannacher and Turek, the constrained NR parallelogram element of Hu and Shi, the P1 element on parallelograms due to Park and Sheen, and the DSSY parallelogram element.