Framework For The A Posteriori Error Analysis Of Nonconforming Finite Elements

Abstract

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 $P_1$ element on parallelograms due to Park and Sheen, and the DSSY parallelogram element.