FrameworkFor The A Posteriori Error Analysis Of Nonconforming Finite Elements

Carsten Carstensen , Jun Hu , Antonio Orlando

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 15

MSC 2000

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

65N15 Error bounds

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.