Framework for the a posteriori error analysis of nonconforming finite elements

摘要

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. The theory is extended to include 1-irregular meshes with at most one hanging node per edge.